台灣地區超載車輛之軸重當量因子研究

(1)

έ៉гડ෹ྶ֘ዃ̝คࢦ༊ณЯ̄ࡁտ

ڒԠጳ ౘઈБ

੼ࡿԫఙጯੰ˿̍͢඀ጯր

ၡ! ࢋ

Ϥٺώ࠷Ϲ఼ณ಼̂јܜĂࡩᑅ੼྿898kPa(130psi)Ăᅈ෹࿅ѝഇనࢍϡ

̝ᇾ໤ࡩᑅ 552kPa(80psi)Ăࠎ˞ଣ੅ࢦ֘෹ྶ৔ᗼĂώࡁտଳϡώ࠷คࢦ෹

ྶቑಛ(62kN~169kN)Ăྻϡѣࢨ̮৵඀ёซҖ֘ᖽᄃᐸෘ˧ጯ̶ژĂ੅ኢྶ

Ѩăคࢦ̈́˧ጯᇴࣃඈᇆᜩણᇴ̝࠹ᙯّĂ֭གྷᙷৠགྷშྮጯ௫੊ቚĂͽ౵̈

ᓁπ͞ᄱम౵ָ̼ޙϲคࢦ༊ณЯ̄(EALF)ሀёĄඕڍ൴னĂࢦ֘෹ྶ၆ྮࢬ

৔ᗼ˜ј4.4~4.5 Ѩೀң৺ᇴгᆧΐĂӈтͽ˟ࢺᇾ໤คࢦ۞෹ྶΙ֘ᔒᑅྮ

ࢬĂዛࢬᐸෘᄃ֘ᖽ৔ᗼ඀ޘΞਕតјᇾ໤คࢦ۞21~23 ࢺĂ෹ྶ৔ᗼ඀ޘΞ

֍˘೹Ą

ᙯᔣෟĈࢦ֘෹ྶăѣࢨ̮৵ᇴࣃ̶ژăᙷৠགྷშྮăEALFĄ

NUMERICAL ANALYSIS IMPLIED EALF UPON OVERLOADING TRUCK IN TAIWAN

Chih-Hsien Lin Wei-Chyum Chen

Department of Civil Engineering Kao Yuan Institute of Technology Kaohsiung, Taiwan 821, R.O.C.

Key Words: overloaded truck, finite-element program, ANN, EALF.

ABSTRACT

Due to rapid growth in the size and weight of heavy vehicles in Taiwan, the highest tire pressure reaches 898kPa (130psi), which exceeds designated tire pressure 552kPa (80psi). The equivalent axle load factor (EALF) using overloading ranging from 62kN to 169kN, based on mechanistic analyses of a finite-element program related to rutting and cracking, axle-load, and loading number, was established by minimum total squared error optimization through Artificial Neural Network (ANN) training and was proposed to analyze overloading effects on flexible pavement in Taiwan. Based on the EALF model in this study, it was found that the growing rate of pavement damage due to overloaded trucks was approximated by the “4.4 or 4.5-power law” progression; thus, two times the standard axle-load rolling on pavement could cause 21 or 23 times the serious damage, for example.

˘ă݈! ֏

઼̰ࢦ֘т̂ఱ֘ăᓑඕ֘ඈĂఈྶ̈́ᇴณܕ˩ѐֽ

ుѐ̙ᕝާిᆧΐĂ֭צז̂ݭ֘ຽ۰۞ܦ༚Ăᐌ඾คࢦă คᇴ۞ᆧΐĂ੼ࡩᑅ۞ֹϡதᐌ̝೩੼Ăֹ଀̂ݭ֘ዃ۞

෹ྶдέ៉ᄃ࣌͟ᆧĂѣᆧ൑ഴĂ੼̳Ԋଂ71 ѐ੓ซҖࠎ

(2)

ഇ̣ѐ۞ྮࢬፋ࣒ࢍထĂҭז 80 ѐྮࢬ˫ు႙ຫᗼ[1]Ă Яѩࢦ֘෹ྶ၆ٺྮࢬ۞ຫᗼ̈́ჯ࣒јώඈЧ͞ࢬ̙Ӏ۞

ଐڶĂ̏ౄј࠹ᙯಏҜӧᕘćᙯٺ఺͞ࢬ۞યᗟĂϫ݈۞

఍ந͞ёĂಶߏд֘ዃྶఱ˯ྮޢĂ઼̳Ԋࠁࣶд੼ి̳

ྮ˯ؠഇгેҖࢦݭ֘ዃ࿅ቀ٩ᑭĄੵ˞ͽ˯ఢቑϡྮ۰

۞͞ڱγĂώࡁտ୬ଂΩ˘࣎֎ޘࢦෛѩีયᗟćдέ៉

ϫֹ݈ٙϡ۞ߘّྮࢬనࢍ͞ڱĂ̪ڻϡ઼γ۞నࢍ͞

ёĂ׎̚˫ͽ઼࡚ AASHTO నࢍڱاкĂҭ֭Ϗ૟ܕѐ

ֽώ࠷෹ྶયᗟЕˢ҂ณĂࡶਕдఢထనࢍ̝ܐ҂ณז෹

ྶ۞৔ᗼĂࠤҌ׎ត̼۞ిޘĂ૟၁ᅫϹ఼ྶࢦͅᑕҌన

ࢍĂ่̙ਕૉ೩੼੼ి̳ྮ۞ڇચਕ˧Ă͞ܮϡྮ۰Ăͽ

྿ְΗΑࢺ۞ड़ڍĂࢫҲ̙υࢋ۞ޙౄ̈́ჯ࣒јώĄ

྽ྮ̝Ϲ఼ณགྷአߤă௚ࢍă̶̈́ژĂೱࠎ࠹༊80kN (18,000 ቀ)ಏคࢦ̝ѨᇴĂჍࠎಏคࢦ༊ณ(equivalent single axle load)ĂᖎჍ ESALĄ֘ዃྶࢦϤ֘ค̶ፉĂࠎค ࢦĄคࢦ෸̂Ă၆྽ྮ̝৔ᗼ඀ޘϺ෸̂Ą࣐ͽಏคࢦ 80kN(18,000 ቀ)үࠎૄ໤Ă૟̙Т෹ྶคࢦҖགྷ྽ྮ߉ࢦ

˘Ѩ၆྽ྮ̝৔ᗼ඀ޘᄃಏคࢦ80kN(18,000 ቀ)߉ࢦ˘Ѩ

ٙౄј۰ј̟ͽͧྵĂ֭Ҥࢍ׎࠹༊80kN (18,000 ቀ)ಏค ࢦ߉ࢦ̝ѨᇴĂჍࠎคࢦ༊ณЯ̄(equivalent axle load factor)ĂᖎჍ EALFĄϹ఼ྶࢦ၆ྮࢬ۞৔ᗼĂॲፂ AASHO

ྏរ྽ྮඕڍពϯ˜јαѨೀң৺ᇴ(fourth power)гᆧ ΐĂӈѣтͽΙ֘ᔒᑅྮࢬ۞ఈࢦᆧΐ˟ࢺĂ݋ዛࢬ৔ᗼ

඀ޘ݋ΞਕߏࣧА۞16 ࢺ(2⁴)[2]ĂϤྤफ़[3-5]̶ژពϯĂ ࢦ֘ྶࢦ̂к෹࿅Ϲ఼щБఢ݋̯ٙధ̝౵̂ࢨטᇾ໤Ă Ч჌ࢦ֘෹ྶதೀͼౌ੼྿ 1.5 ࢺͽ˯ćΗᓑඕ֘෹ྶᗕ คࢦ̂ࡗะ̚д20.5 ጟ~22 ጟมĂБᓑඕ֘෹ྶᗕࢦะ̚

д25.5 ጟ~30.5 ጟมĂ෹ྶࡩᑅ౵̂੼྿ 898kPa (130psi)Ą ߇ϫ݈Ι֘ࡩᑅ࠰̏ᅈ੼ٺ AASHO ྏរ྽ྮٙϡ۞

552kPa (80psi)Ăࢦ֘෹ྶٙΞਕౄј۞ዛࢬ৔ᗼ၆ዳ᜕ొ

ܝ҃֏૟ߏ˘ีՕࢦ۞࢑ፉĄ

ώࡁտྻϡˬჯѣࢨ̮৵඀ёůABAQUS [6]ซҖዛ ࢬ̶ژĂͽྋژࠎ͹۞͞ڱ(analytically-based method)ޙϲ คࢦ༊ณЯ̄(EALF)Ă֭ซ˘Վଣ੅คࢦѨᇴăᑛࢦ̈́˧

ጯᇴࣃඈᇆᜩЯ৵̝࠹ᙯّĂ֭·Њͧྵ̙ТᘒܦՄफ़̝

ᇆᜩड़ᑕĂͽ௑Ъ઼̰੼ి̳ྮዛࢬనࢍ̝ᅮՐĄ

˟ăคࢦ༊ณЯ̝̄ႊซ

คࢦ༊ณЯ̄(equivalent axle load factor, EALF)Ă૱జ

༊јෞҤ֘ዃคࢦٙౄјዛࢬ৔ᗼ۞໤݋Ăೱ֏̝Ăӈд

྽ྮఢထనࢍ̝ܐӀϡ࠹ᙯ۞ࢍზ̳ёĂͽ˘ಏคࢦ 80-kN(18-kip)ࠎᇾ໤คĂࢍზ࠹Т۞ᒖဩЯ৵̈́ዛࢬ୧І

˭Ă̙Тคࢦ࠹༊ٺѩᇾ໤ค၆ٺྮࢬ৔ᗼ۞඀ޘĄEALF

ੵྫྷคࢦٕͧคѨᇴͧѣᙯĂధк൴णዛࢬݓޘ̶ژᄃన

ࢍ͞ڱ۞ࡁտ፟ᙯᄃጯ۰ĂϺဘྏͽᘒܦᆸغొ̝ͪπૺ

ᑕតٕྮૄ౤ბ̝ݬۡᑅᑕតĂ၆ᑕྮࢬ྿ז৔ᚓ̝ྶࢦ ࢦኑѨᇴ۞ᙯܼĂүࠎޙϲEALF ֶ̝ፂĄͽ˭ᖎࢗ EALF

͹ࢋ൴णڻࢭĄ

1. Deacon (1969) [ 7 ]

઄నࡩᑅତᛈࢬ᎕ࠎ๪ԛĂତᛈࡩᑅӮ̶̹Ҷٺତᛈ ࢬ᎕˯ĂӀϡChevron ࿪ཝ඀ё̶ژĂଯጱ΍ዛࢬি౻৔

ᗼ˭̝คࢦ༊ณЯ̄Ĉ

4

18

18 









=

=

t tx

Nx

EALF N

ε

ε (1)

2. AASHTO (1972) [ 8 ]

ଯጱ΍ࢍზคࢦ༊ณ۞ਫ਼ᕩёĂт̳ё(2)Ă(3)ٙϯĈ

β β ₁₈

2 2

18

log 33 . 4 ) log(

79 . 4 ) 1 18 log(

79 . 4

log L L L G G

N

N t

x x t

x= + − + + + −

 





(2)



 





−

= −

5 . 1 2 . 4 2 . 4 log ( p

Gt ^t (3a)

( )

( )⁵^.¹⁹ ³₂^.²³

23 . 3 2

1 081 . 40 0 .

0 SN L L L_x

x +

+ +

=

β (3b)

༊L_xඈٺ18ĂL₂ඈٺ1 ॡĂ΃ˢ(3b)ࢍზ଀זβ₁₈ĄЯ ѩĂ଀΍˭Еᙯܼё(4)Ĉ

Nx

EALF=N¹⁸ (4)

3. Ramsamooj et al. (1972) [ 9 ]

ͽ৔ᗼ˧ጯநኢ̶ژߘّዛࢬ۞৔ᗼ׶ি౻ෘᓀ࠹

ᙯયᗟĂֶPari ؠޠጱ΍˭ё(5)ĂЯѩГӀϡಏคྶࢦͧ

۞4 Ѩ㌇Ѩ͞ࢺᇴՐ଀คࢦ༊ณЯ̄Ą

AK4

d d

n

c = (5)

4. Terrel et al.(1976) [10]

҂ᇋ዇ࢦĂ׽ؠࡩᑅ׶ᗕ዇ᆵ 10 ࡻЦĂࢬᆸݓޘ 6

ࡻЦĂ֘ి10mph ͽ̈́ዛࢬ໢ޘ 68.5ƩඈЯ৵۞ᇆᜩĂགྷ CHEV 5L ࿪ཝ඀ё̶ژྍዛࢬצྶࢦࢦኑѨᇴҌ৔ᗼࠎ

ͤĂ଀זᘒܦᆸغొशШٛᑕត׶ྮԖ౤ొݬۡᑅᑕតĂ Гଯጱ΍คࢦ༊ณЯ̄Ĉ











= Nx

EALF N¹⁸ (6)

5. ΔለЪүࡁտࢍထ(1977) [11]

дΔለЪүࡁտࢍထ̚ĂӀϡAASHO ྏរ྽ྮඕڍ ଯጱ΍คࢦ༊ณЯ̄׶คࢦͧࣃ۞n Ѩ͞јϒͧĂт˭ёĈ

(3)

ܑ˘ ˣ჌ࢦ֘჌ᙷ̈́׎ڱؠࢦณ

TS -

TD -

T3 - -

T4 - -

T5 - -

F4 - -

F5 - -

10 14.5

10 14.5 14.5 14.5 14.5

15 21

35

42

n x

L EALF L 









=

18

(7)

6. Southgate et al.(1984) [ 1 2 ]

ӀϡᑕតਕW ᖼೱјᑕតΑ(work strain) ewͽՐྋዛ ࢬি౻۞યᗟĂ׎̚E ࠎ໅ͩᇅّሀᇴĂт˭ёĈ

5 .

2 0



 



= E

e_w W (8)

Ӏϡ˯ёΑਕ̢ೱޢĂͽਫ਼ᕩё(9)Ă(10)Ր଀ᘒܦᆸ غొٛᑕតε ̈́ྶࢦࢦኑѨᇴ NĂ΃ˢ(11)଀זคࢦ༊ณ_t Я̄Ą

( ) ¹^.¹⁴⁸³^log( ) ⁰^.¹⁶³⁸

logε_t = e_w− (9)

( ) ⁶^.⁴⁶³⁶^log( ) ¹⁷^.³⁰⁸¹

logN =− e_w − (10)

Nx

EALF=N¹⁸ (11)

7. ઼࡚ᘒܦםົ(1991) [13]

AI ֘ᖽሀё઄న֘ᖽயϠٺྮૄᆸĂ׎ዶЧᆸ̝ϖ˳

តԛณ̟ͽنரĂ׎ሀётё(12)Ą׎̚Ăε_roadbed ࠎྮૄ

౤ొ̝ݬۡᑅᒺᑕតĂN_rutࠎ֘ᖽ৔ᗼॡ̝ͅᖬྶࢦѨ ᇴĄѩሀё̝ϖ˳តԛ৔ᗼࣃࠎ13~19mm (0.5~0.75 in)Ă ӈϖ˳តԛ৔ᗼͧࣃࠎ100%ॡĂٙ၆ᑕ̝֘ᖽࣃĄ

477 . 4

9 ( )

10 365 .

1 × ⁻ × ⁻

= roadbed

Nrut ε (12)

AI ᐸෘሀёܼ˜ॲፂனಞ៍ീྤफ़൴ण҃΍Ăтё (13)ٙϯĄ׎̚ĂN_crkࠎᐸෘ৔ᗼயϠॡ̝ྶࢦͅኑѨᇴĂ Eacࠎᘒܦ஄጖˿̝ᇅّሀᇴ(psi)Ăε ࠎ AC ᆸغొͪπૺ_t ᑕតĄ

363 . 2 671 .

5 ( )

) ( 0685 .

0 × ⁻ × ⁻

= t ac

crk E

N ε (13)

TS 41.48%

TD 6.67%

T3 4.32%

T4 37.88%

T6 6.01%

F4

0.40% F5 3.24%

ဦ 1 Ч჌֘჌คѨटณ̶Ҷ

ˬăࡁտ͞ڱ 1. ќ෱৭ࢦ֘෹ྶ̶ژ

֘ዃఈࢦྤफ़Ăࠎ̳ྮซҖనࢍăዳ᜕ăჯ࣒ඈ̍ү

̝ࢦࢋֶፂĄዛࢬົЯڇચ֘ዃఈࢦ̂̈҃ѣځព̝̙Т ᒻड़Ąֶώ࠷ĶϹ఼щБఢ݋ķௐˬ˩ˣ୧̈́Ķ੼ి̳ྮ

Ϲ఼გטఢ݋ķௐ˩˝୧੼ి̳ྮՠ֘ࢨטఢؠĂ౵̂ค ࢦఢؠࠎૄ໤Ĉಏคࢦࠎ10 ጟĂᗕคࢦࠎ 14.5 ጟĂ઼࡚

ᓑ֣߆عэᅫ̳ྮՠ̝֘౵̂ಏคࢦࢨטࠎ׌༱ቀ(ࡗ 10 ጟ)Ăᗕคคࢦࠎˬ༱αΖቀ(ࡗ 17 ጟ)Ă෹΍౵̂ࢨט̝֘

ዃืϦኛᓜॡ఼Җᙋᄃԧ઼࠹ТćГֶ੼̳Ԋ̝ࢦ̶֘

ᙷĂΞ̶јಏវ̂ఱ֘(TSăTD)ăΗᓑඕ֘(T3ăT4ăT5)

̈́Бᓑඕ֘(F4ăF5)Ăтܑ˘ٙϯ[3-5,14]Ą

ࢦݭ֘ዃ̝ྶࢦϫ઼݈̰ྵԆፋ̝ࢦݭ֘ዃྤफ़Ă༊

ᛳ੼̳ԊϤ̳ྮᛋ၅੨Ъ͔ጱ֘ዃዺˢгቀ৭צᑭĂՏѐ

׌Ѩ(Ч˘͇)ؠഇ၁߉̝คࢦăคѨአߤĄ

ώࡁտܼӀϡϔ઼83~87 ѐ઼̰ѱͤăЬ֧ăࣶڒ̈́

ت̋ќ෱৭ࡗ225,000 ඊ̝Чᙷࢦ֘ᐖၗгቀคѨአߤྤ

फ़Ăᘱᄦјтဦ 1Ą׎̚Ăಏវ̂ఱ֘ͽ TS ҫٙѣ֘ݭ 41.48%౵кĂΗᓑඕ֘݋ͽ T4 ̝ 37.88%ĂБᓑඕ֘ F5

̝3.24%౵׍΃ّܑ[3,14]Ą

ӀϡЧќ෱৭̝Чᙷࢦ֘ᐖၗгቀคѨአߤྤफ़ᘱ ᄦјคࢦคѨ̶ҶဦĂͽ͞ܮ࠻΍ࢦ̝֘ྶࢦଐԛĂ่

ЕᓝЧ΃ܑ֘჌Ĉಏវ̂ఱ֘ TSăΗᓑඕ֘ T4 ̈́Бᓑ ඕ֘F5Ăᄲځ׎คࢦคѨ෹ྶᄃϏ෹ྶ̶Ҷဦ 2ĄTS ̝ คࢦ̂ࡗะ̚д3.5 ጟ~5.5 ጟ̝มĂᔵѩ֘ݭ෹ྶͧத̙

੼Ă൒҃׎ҖዺคѨᇴ੼Ăࠎ͹ࢋҖዺ̝֘ݭĄဦ 3 Η ᓑඕ֘T4 ͹ࢋٚࢦคдٺޢคĂ׎ݭёࠎಏůಏůᗕค ˣ዇Ăဦ̝̚Чќ෱৭̶Ҷѡቢѣځពะ̚ன෪Ăд෹

ྶคࢦ̂ࡗะ̚д 20.5 ጟ~22 ጟมĂ׎คѨͧத੼Ăྍ

֘ݭдݑొ૯̋ќ෱৭ֹϡதᅲ੼Ă૟ౄјᚑࢦ۞ዛࢬ

৔ᗼĄဦ4 Бᓑඕ֘ F5 ͹ࢋߏϤௐ˟ค௡ֽٚצྶࢦĂ

׎ݭёࠎಏůᗕůᗕค˩዇Ą׎̚ĂF5 ֭Ϗ΍னٺѱͤă

ࣶڒќ෱৭Ă̶ҶѡቢӔ೸ใன෪൑ځព۞ะ̚ડાĂ Ϗ෹ྶొ̶јᗕपېၗĂ҃෹ྶྵځពะ̚д 25.5 ጟ

~30.5 ጟ۞ቑಛĄ

(4)

1500 1200 900 600 300 0

0.5 5.5 10.5 15.5 20.5 25.5 30.5 35.5 10

ဦ 2 ಏវ̂ఱ֘ TS Чќ෱৭̝คࢦคѨ̶Ҷ

500 400 300 200 100 0

0.5 5.5 10.5 15.5 20.5 25.5 30.5 35.5 40.5 14.5

ဦ 3 Ηᓑඕ֘ T4 Чќ෱৭̝คࢦคѨ̶Ҷ

ࡶซ˘Վ੅ኢЧ֘჌ٺЧќ෱৭̝෹ྶ̶Ҷன෪Ăώ ࡁտͽ̳ё(14)̈́(15)ࢍზ΍Чᙷࢦ֘(В˛჌֘ݭ)۞෹ྶ

πӮࣃ̈́෹ྶதĈ෹ྶπӮࣃߏ૟คࢦคѨ̶Ҷဦ̚෹࿅

ڱؠఢቑࣃొ̶คࢦ(X_i′)คѨ(Yi′)۞ࢷ᎕ Σ(Xi′×Yi′)ੵͽ 5 ѐ̰۞ᓁคᇴ(ΣYi′)Ăтဦ 5 ̝ϯຍဦć҃෹ྶத۞ؠཌྷߏ дคࢦคѨ̶Ҷဦ̚෹࿅ڱؠఢቑࣃ۞คࢦᓁ׶ੵͽ5 ѐ

̰۞ᓁคࢦĄֶፂЧ̳ёΞᘱᄦтဦ6 ٙϯĄ

) (

5

) ) (

(

i i i

Y Y

∑ X ×

=

= ×

คѨ ѐ̰෹࿅ఢቑࢦ̝֘ᓁ

ᓁ׶

คѨ คࢦ

෹࿅ఢቑ̝ࢦ֘

ጟ

෹ྶπӮࣃ

(14)

ѐ఼̰࿅ࢦ֘ᓁคѨ

෹࿅ఢቑ̝ࢦ֘ᓁคࢦ

෹ྶத(%)= 5 (15)

2. ொજྶࢦ̝నؠ

д̶ژዛࢬඕၹ̝݈ĂࢵАυืޙϲዛࢬ̶ژሀёĂ ώࡁտͽABAQUS[6]ࠎ̶ژ̍׍ĂྶࢦԛёࠎொજྶࢦĂ

҃ఈࢦ۞̶̝Ҷ̬ٺѣࢨ̮৵༼ᕇᄃ༼ᕇ̝ม݋઄నјቢ

ّᙯܼĂͽဦ7 ̂ரࢗຍ[14]ĄϤٺ ABAQUS ֹٙϡ۞જ

30

20

10

0

0.5 5.5 10.5 15.5 20.5 25.5 30.5 35.5 40.5 14.5

ဦ 4 Бᓑඕ֘ F5 Чќ෱৭̝คࢦคѨ̶Ҷ

50 40 30 20 10

0 x'

Y'

X'_i

Y'_i

ဦ 5 ෹ྶπӮࣃࢍზᄲځဦ

ၗ̶ژ޽΄͹ࢋߏдॡมા˯ĂЯѩဦ1 ۞۩ม៍هυื

ॲፂిޘ̂̈Ă̈́዇ࡩ۞ତᛈܜޘĂᖼೱјॡม።඀ซҖ

ொજྶࢦ̝જၗ̶ژĄ༊֘዇఼࿅ߙ˘ᕇॡĂͽ˘ܕҬୗ

ԛ۞ဦԛĂтဦ 8Ăֽೡࢗѩ֘዇఼࿅ѩᕇॡٙ߉ͽ۞ྶ

ࢦᄃॡมĄ

3. ዛࢬ̶ژ̝შॾޙϲ

д̷౷შॾొЊĂྵ͎̈̇۞ѣࢨ̮৵შॾΞ೩ֻྵ

ࠎჟቁ۞̶ژĄЯѩĂώࡁտдྶࢦᇆᜩቑಛ̰XăY ͞ Ш࠰ଳϡඈᆵޘშॾĄֶ̋̚੼઼྽ዛࢬඕၹనؠݓޘĂ

྽ྮሀݭ̷౷ͽ֘ዃγ዇ࠎૄ໤ଳ֘྽νăΠΗ၆Ⴭ(1.9

̳͎)̶ژͽ༼࠷̶ژॡมĂγ֘྽ᙝࠧ୧Іଳݬۡ Z Шࠎ ҋϤბĂ၆Ⴭค݋ XăZ ࠎҋϤბćТॡࠎৌ၁ሀᑢҖ֘

࢖ྫҜཉ̝੨ЪĂפγ֘྽γᇾቢࡗ85 ̶̳఍ࠎγ֘዇Ҝ ཉĂтဦ9 ٙϯĄ

ዛࢬሀݭӈͽΗᓑඕΙ֘֘ܜ(50 ӏ=15.2 ̳͎)ࠎన ؠܜޘĂтဦ10 ٙϯ[14]Ąֶ˯༼Ι֘Җዺిޘ̈́ொજྶ

ࢦనؠࢋᕇĂ࠰߉ͽѩ˘ܕҬୗԛ۞ྶࢦሀᑢ͞ёĂтဦ 11Ą

4. ዛࢬЧᆸՄफ़ّኳ̝నؠ

(˘) ࢬᆸՄफ़ᇅّሀᇴĈᘒܦՄफ़ࠎ˘ᕆᇅّՄफ़ĂՄफ़

۞ᕆᇅপّᄃॡม̈́໢ޘѣᙯĂ̙Т۞၁រᇴፂϒΞ

(5)

35 30 25 20 15 10 5

0 TS TD T3 T4 T5 F4 F5 100

80

60

40

20

0

%

35 30 25 20 15 10 5

0 TS TD T3 T4 T5 F4 F5 100

80 60

40 20

0

%

35 30 25 20 15 10 5

0 TS TD T3 T4 T5 F4 F5 100

80

60

40

20

0

%

35 30 25 20 15 10 5

0 TS TD T3 T4 T5 F4 F5 100

80

60

40

20

0

%

ဦ 6 Чќ෱৭෹ྶத̝ͧྵဦ

Load amplitude

loading time 1.0

ဦ 7 ྶࢦሀᑢ઄నϯຍဦ

Load amplitude

1.0

loading time 1

2

ဦ 8 ֘዇఼࿅ߙ˘ᕇॡ̝ୗԛྶࢦॡมሀᑢဦ

Profile

Top view

(half-infinite elements)

(150mm) (200mm) (300mm) (750mm) 5×17cm4×5cm 5×17cm

Y Z

Y X

20 elements @264mm

ဦ 9 Җ֘࢖ྫ̝྽ྮѣࢨ̮৵შॾ̷౷

ͅᑕ΍̙ТՄኳă̙Т໢ޘ˭ᘒܦ஄጖˿۞ᕆᇅপ

ّĄώࡁտଳϡ੫ˢޘ40/50(Pen40/50)ă੫ˢޘ 60/70 (Pen60/70)̈́Լኳ I ݭ(MA I)ඈˬ჌ᘒܦՄफ़Ăٺ၁រ

(6)

15.2m(50’)

X Y 3.8m

ဦ 10! ொજྶࢦ̝ዛࢬሀݭࢼෛဦ

X Z

ဦ 11! ୗԛொજྶࢦ̶ژሀݭ̝ϯຍဦ

ވซҖಏคሕតྏរĂͽྏរྤफ़ྻϡ ABAQUS ̝ Viscoelastic ޽΄నؠᕆᇅّኳ̝ᏮˢણᇴĂЕٺܑ˟

̚Ăٙϯᇴࣃࠎሕតΐྶ0.1sec ̝ᇅّሀᇴࣃĄѩγĂ ॲፂѣࢨ̮৵̝ᑕ˧ᑕត̶ژĂࡶՄफ़෹࿅ໂࢨૺᑕ

˧ٕૺᑕតĂயϠ৔ᗼĂྍ̮৵൑ٚྶਕ˧Ăԛјෘ

ᓀĂЯѩٺ߉ΐ˭˘คࢦᆧณ݈ੵΝ̏৔ᗼ̝̮৵Ă Гᚶᜈ߉ΐคࢦĂᑕ˧ົࢦາ̶ҶĂۡҌՄफ़৔ᗼҌ ᘒܦᆸغొĄώ͛ᐸෘ৔ᗼ(fatigue cracking)ሀё̝

AC ࢬᆸغొͪπૺᑕត(εt)ҿؠᇾ໤тܑˬĄ (˟) غᆸăૄᆸ̈́ྮૄᇅّሀᇴĈܑαࠎዛࢬඕၹ̚غ

ᆸăૄᆸ̈́ྮૄ̝ᇅّሀᇴࣃϺࠎABAQUS ซҖ˧

ጯ̶ژॡٙᅮࢋ۞غᆸăૄᆸ̈́ྮૄՄफ़ّኳ۞ૄ

ώྤफ़Ą

5. คࢦ༊ณЯ̄(EALF)̝ଯႊ

д݈ࢗ͛ᚥаᜪ̬ٙ௜۞คࢦ༊ณЯ̝̄நኢࡦഀ

̈́ଯጱ៍هĂՏҜጯ۰ٕࡁտࢍထٙ҂ᇋ۞ણᇴ̙ԆБ˘

࡭Ă࠰ѣ׎ֶፂ۞நኢࡦഀĂҭ׎ᙯܼё̚జ͔ϡֽؠཌྷ EALF ۰Ă̂кᇴͽคࢦͧăᑕតٕͧྶࢦѨᇴͧඈࠎ͹

ࢋ҂ณĂтܑ̣ٙϯĄ͛ᚥ̚Чछጯ۰۞៍هĂ֭՟ѣޝ

୻຾ٕߏۡତгᄲځEALF ᄃคࢦăྶࢦѨᇴ̈́˧ጯણᇴ

̝ม۞ᙯܼĂּт઼γጯ۰Deacon[7]ᄃ Ramsamooj ඈˠ [9]ĂͽྶࢦѨᇴᄃ˧ጯણᇴٕคࢦͧத۞៍هֽܑϯ EALFĂ׎̚㌇Ѩ͞ࢺᇴ࠰ࠎ 4 ࢺ㌇Ѩ͞ć఺ᇹ۞ଯႊ࿅඀

̙֭˘ؠዋϡٺώ࠷ࢦ֘෹ྶன෪̝৔ᗼෞҤĂͷ఺ᇹ۞

ܑ˟ ᘒܦ஄጖˿ࢬᆸᇅّሀᇴ[14]

ᘒܦՄफ़჌ᙷ ዛࢬ໢ޘ

Pen40/50 Pen60/70 MA I 25ƨ

60ƨ

5,978 7,466

18,974 3,090

28,657 7,847

ොĈಏҜkg/cm²

ܑˬ ᘒܦ஄጖˿Մफ़̝ᐸෘ৔ᗼᓜࠧࣃ[14]

ᘒܦՄफ़჌ᙷ ዛࢬ໢ޘ

Pen40/50 Pen60/70 MA I ໂࢨૺ˧ૻޘ

ໂࢨૺᑕត

13 500×10^-6

12 1000×10^-6

14 500×10^-6

ොĈಏҜkg/cm²

ܑα! غăૄᆸ̈́ྮૄ̝ᇅّሀᇴ[14]

ዛࢬඕၹ Մ! फ़ ώࡁտ

غᆸ

ૄᆸ

ྮૄ

гᘒܦ఍ந ༤Ϯ৺੨௕फ़

ྮಟ

21,120 1,760

845

ොĈಏҜkg/cm²Ăغᆸ໢ޘ25ƨ

ܑ̣ คࢦ༊ณЯ̄ EALF ̝నࢍநه నࢍநه ͛ᚥֽ໚ ൴ण̳ё

ྶࢦѨᇴͧ

ůᑕតͧ

Deacon (1969) Terrel ඈˠ (1976) Outhgate ඈˠ (1984)

4 18

18 

 



=

= ε

ε

t tx

Nx

EALF N

ྶࢦͧ

Ramsamooj ඈˠ (1972) ΔለЪүࡁտࢍထ

(1977)

4 18

 



= L EALF L^x

ྶࢦѨᇴͧ

AASHO ྏរ྽ྮ

(1972)

઼࡚ᘒܦםົ(1991) N EALF N

x

= 18

ᙯ่ܼዋϡٺি౻͞ࢬ۞࿰ീĄ੫၆ώ࠷੼໢˭̝ࢦ֘෹

ྶĂώࡁտ૟੫၆ᐸෘ̈́֘ᖽ̶ࢗ੅ኢĂॲፂࡁտ[3]޽

΍ĂϤٺྶࢦΪдᘒܦࢬᆸ౤ొݬۡᑅᑕតѣព඾۞ត

̼Ă׎΁Чᆸ̝ݬۡᑅᑕត࠰̙ځពĂ߇ώࡁտ͹ࢋ੫၆ ࢦ֘Җश࢖ྫ̝ᐸෘ̈́֘ᖽ࠹ᙯҜཉซҖ˧ጯ̶ژĈዛࢬ

໢ޘ25ƨĂ዇͕̚˭̝͞ᘒܦࢬᆸغొ̝ͪπૺᑕត(ε_t) ࠎዛࢬᐸෘ̝҂ณĂ֘ᖽ݋҂ณዛࢬ໢ޘ60ƨॡ዇͕̚˭

̝͞ᘒܦࢬᆸ౤ొݬۡѨᄃ˧ጯᇴࣃ࠹၆ᑕ۞ᙯܼĂт̳

ё(16)ĂඕЪคࢦ-คࢦѨᇴ-˧ጯᇴࣃˬ۰ᙯܼĂᗃ୻׎̚

۞ሀቘᕇ[15,16]ĄӀϡ఺ֱͧࣃ۞㌇Ѩٕ͞۰ቢّਫ਼ᕩ ёĂྻϡᙷৠགྷშྮޙϲ੊ቚᑫĂ࢜΃ќᑦ̶ژϹ̢ᇆᜩ

̝࠹ᙯّĄ֭ซ˘Վͽ౵ָ̼ޙϲ׍ѣ΃ّܑ̝EALF ሀ ёĂͽ௑Ъέ៉ዛࢬ၁ᅫېڶĂֻྮࢬనࢍ̝ࢦ֘෹ྶෞ

(7)

Ҥ̝ણ҂ֶፂĄ











= Nx

EALF N¹⁸ คࢦѨᇴ៍ه (16a)

















































































































= _n

tx n

t b

cx b

c

m m or a

a

ε ε ε

ε

1 1

18 18

n

t tx b

c

cx or 





















=

18

18 ε

ε ε

ε ˧ጯᇴࣃ៍ه (16b)

q x d

x

L or L L

L























=

18 18

คࢦ៍ه (16c)

αăඕڍᄃ੅ኢ

ώ༼੅ኢ۞ࢦᕇ̶ј֘ᖽᄃি౻ᐸෘ̝৔ᗼ̶ژĂ֭

ᄲځ EALF ࠹ᙯણᇴ̝คѨăคࢦ̈́˧ጯᇴࣃඈˬ۰ᙯ

ܼĂᗃ୻׎̚ጕѨ͞ࢺᇴ̝ሀቘᕇĄ

1. ྶࢦѨᇴ N ࣃ̈́׎ᑕត̝ࢍზ

ֶ˯ࢗΞۢĂώ࠷Ηᓑඕ֘෹ྶᗕคࢦ̂ࡗะ̚д 20.5 ጟ~22 ጟมĂБᓑඕ֘෹ྶᗕคࢦะ̚д 25.5 ጟ~30.5 ጟมĂЯѩტЪ҂ณ෹ྶᗕคࢦቑಛࡗ20 ጟ~32 ጟĂࠎܮ ٺѣࢨ̮৵඀ё၆ჍሀᑢĂ੨Ъဦ9 ̝γ֘዇Җ֘࢖ྫҜ ཉĂ่҂ᇋያγ֘ቡ̝෹ྶಏคࢦĂ݋ࡗࠎ10 ጟ~16 ጟมĄ Яѩώࡁտଳפ62kN~169kN(6.4 ጟ~17.3 ጟ)Ăӣᇾ໤ಏค ࢦ80kN(18kip)Ăࠎώ࠷ࢦ̝֘ಏคࢦ෹ྶቑಛĂТॡֶፂ

˯ࢗABAQUS ඀ёాᜈᝑ΃(recursive)̝ѣࢨ̮৵ሀᑢా

ᜈொજྶࢦĂ̶Ҿࢍზ଀΍̙ТᘒܦՄफ़̝ᐸෘคѨ ( Ncrk)ᄃ֘ᖽคѨ( Nrut)Ă̈́၆ᑕ̝ 25ƨᘒܦࢬᆸغొ̝

ͪπૺᑕត(ε_t)ᄃ 60ƨᘒܦࢬᆸ౤ొᑅᒺᑕត(ε_c)Ă̶ژ ඕڍтܑ̱ᄃܑ˛Ąࠎ˞͞ܮͧྵˬ჌ᘒܦՄफ़̝คѨᄃ ᑕតมᙯܼĂ૟ܑ̱ᄃܑ˛̶Ҿᘱᄦјᐸෘᄃᐸෘ̝ࢷ㌇

ѡቢĂтဦ12 ̈́ဦ 13ĄϤဦ 12 ̚൴ன Pen40/50 ᄃ MAǵ

˟჌ᘒܦՄफ़۞ি౻ᐸෘࢷ㌇ѡቢᅲࠎତܕĂ҃Pen60/70 ᘒܦϤٺՄफ़ώ֗׍ྵ̂੫ˢޘ̈́ؼणّĂΞٚצྵ̂۞

ૺ˧ĂЯѩдᐸෘคѨ N_crk˭Ξٚצྵ̝̂ε_tĄ࠹၆ᑕٺ ဦ13ĂPen60/70 ᘒܦՄफ़۞ѡቢ୆தត̼ྵԣĂPen40/50

׶MA I ۞ѡቢ݋ྵࠎπቤĂពϯֹϡ Pen60/70 ᘒܦՄफ़ ԩតԛ̝ᕆᇅّྵमĂЯѩ֘ᖽ৔ᗼ۞ిޘͧ੓Ωγ׌჌

Մफ़ֽ଀֝ిĄ˭༼૟ତᜈ੅ኢˬ჌ᘒܦՄफ़̝ٺᐸෘ(ԩ

ૺ)ᄃ֘ᖽ(ԩតԛ)̙ТคࢦăคѨ̈́˧ጯᇴࣃ̝ม۞࠹ᙯ

ّĂ֭ޙϲคࢦ༊ณЯ̄(EALF)Ą

ܑ̱ ᐸෘ̶ژ̝คѨN_crk̈́၆ᑕ̝ε_t Ncrk (×10⁶) εt(×10^-5) ಏคࢦ

(kN) Pen40/50 Pen60/70 MA I Pen40/50 Pen60/70 MA I 62

80 98 116 134 151 169

9190 2934 1183 554 290 165 100

4519 1466 593 280 147 84 52

7405 2399 968 454 238 136 83

4.43 5.70 6.95 8.22 9.48 10.75 12.02

7.05 9.06 11.07 13.08 15.09 17.11 19.12

4.96 6.37 7.79 9.20 10.62 12.04 13.45

ܑ˛ ֘ᖽ̶ژ̝คѨN_ruẗ́၆ᑕ̝ε_c Nrut(×10⁶) εc(×10^-4) ಏคࢦ

(kN) Pen40/50 Pen60/70 MA I Pen40/50 Pen60/70 MA I 62

80 98 116 134 151 169

1332 436 178 85 46 27 17

358 119 50 25 14 8 5

1428 466 191 91 49 29 18

1.46 2.04 2.62 3.20 3.79 4.37 4.95

6.22 7.58 10.16 12.12 14.09 16.07 18.04

1.25 1.77 2.29 2.82 3.34 3.86 4.38

2. คࢦѨᇴ-คࢦ-˧ጯᇴࣃ̝࠹ᙯّ

ࠎ˞ซ˘Վଣ੅EALF ̚ྶѨăคࢦᄃ˧ጯᇴࣃඈЧ ણᇴ̝࠹ᙯّĂ૟ܑ̱ᄃܑ˛คࢦăᑕតᄃྶࢦѨᇴᖼ̼

ࠎคࢦͧăᑕតͧᄃคѨͧĂтܑˣᄃܑ˝Ă׎̚Ăᐸෘ

̶ژٙౄј۞คѨᇆᜩர̂ٺ֘ᖽĄϤܑˣᐸෘ̶ژΞ࠻

΍Ăคࢦͧᄃ࠹၆ᑕ̝ᑕតͧ࠹म൑ೀĂГ૟คࢦͧ(L_x/L₁₈) ᄃคѨͧ(N₁₈/ N_x)ᘱᄦјဦ 14ĂϤဦΞ୻຾៍၅΍คࢦͧ

ᄃคѨ̝ͧត̼ᙯܼĂ൴னѡቢೀͼࢦЪĂពϯྮࢬצז ѩࢦ֘෹ྶಏคቑಛ 62kN~169kN(6.4 ጟ~17.3 ጟ)үϡ

˭Ăˬ჌ᘒܦՄफ़ٺᐸෘ̝৔ᗼᔌ๕ߏ࠹ܕ۞Ą

൒҃Ăܑ˝֘ᖽ̶ژ̚คࢦͧᄃˬ჌ᘒܦՄफ़̝ᑕត

ܑͧன̙֭࠹ТĂͷ̙ТᘒܦՄफ़ٺคѨүϡ˭Ă֘ᖽܑ

னϏႽ˘࡭ĂͽPen40/50 ᘒܦՄफ़ࠎּĂಏคࢦ 169kN ү ϡٺྮࢬॡĂྶࢦͧ(L_x/L₁₈)ࠎ 2.11Ăᑕតͧ(ε_cx/ε_c18)ࠎ 2.43Ă

ྶࢦͧ׶ᑕត֭ͧܧј˘ؠ۞ᙯܼĂᐌ඾ಏคࢦᅍᆧĂᑕ តͧᆧΐ۞ిޘͧྶࢦֽͧ଀ԣĂֶܑ˝̚(N_c18/ N_cx)ᇴፂ ពϯࠎ25.65Ă࠹༊ٺಏค 80kN үϡٺྮࢬٙౄј۞৔ᗼ

̝25.65 ࢺĄГ૟คࢦͧ(L_x/L₁₈)ăᑕតͧ(ε_cx/ε_c18)ᄃคѨͧ

(N₁₈/N_x)Тॡᘱᄦјဦ 15ĂϤဦΞ୻຾៍၅΍֘ᖽ৔ᗼ͞

ࢬĂคࢦͧăᑕតͧᄃคѨ̝ͧࢷጕᙯܼ̙֭˘࡭Ă߇ࡶ

ۡତ઄ؠEALF ̝㌇Ѩ͞ࢺᇴ࠰ࠎ 4Ă݋൑ڱͅᑕѩࢦ֘

෹ྶಏคቑಛ 62kN~169kN(6.4 ጟ~17.3 ጟ)үϡ˭֘ᖽৌ

၁ېڶĄΩγĂࡶଂ෹ྶ۞֎ޘֽ࠻Ăтဦ15ĂಏคࢦϤ 62kN(14kip)੓Ăͽ 18kN(4kip)ֶԔᆧΐࡗҌ 1.23 ࢺᇾ໤ค 80kN ޢĂٙயϠ۞คѨͧͽܧ׽ؠּͧᆐধᅍᆧĂᔵ൒ᆧ ΐ۞ిޘົు႙ᔌٺቤ׶ᘦؠĂҭѩॡྮࢬѝ̏৔ᗼĂಉ

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1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 Ncrk

0 5 10 15 20 25

£‘t (*10^-5)

Pen 40/50 Pen 60/70 MA I

ဦ 12 คѨ Ncrkᄃε_t̝ᙯܼဦ-ᐸෘ̶ژ

1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 Nrut

0 5 10 15 20

£‘c (*10^-4)

Pen 40/50 Pen 60/70 MA I

ဦ 13 คѨ Nrutᄃε_c̝ᙯܼဦ-֘ᖽ̶ژ

30

20

10

0

Pen 40/50 Pen 60/70 MA I

0 0.5 1 1.5 2 2.5

tx / t18

Nt18/Ntx

ဦ 14 ᑕតͧᄃคѨ̝ͧࢷ㌇ᙯܼဦ-ᐸෘ̶ژ

ε׎ࣧѣ۞ڇચͪ໤˞Ą

ࡶ૟ဦ14 ᄃဦ 15 ၆ᑕٺဦ 12 ᄃဦ 13Ăޢ۰ྵਕ࠻

΍ᘒܦ჌ᙷ၆ٺዛࢬᒻड़۞ត̼ᇆᜩĂ൒҃Ăѩᕇඕኢ֭

̙Ϭ࠼ĂЯࠎࢍზEALF ॡĂ࠰ߏͽᇾ໤ಏค 80kN(18kip)

ٕ׎ٙጱ࡭۞ᑕតણᇴүࠎ̶ϓĂтё(16b)ᄃё(16c)Ă఺

ߏд׽ؠՄफ़ણᇴ۞ଐڶ˭ٙࢍზ΍ֽ۞Ч჌ඕڍĂ҃ˬ ۰̝ٺྮࢬᒻड़۞ᐹК඀ޘ݋̙֭˘࡭ĄტЪ˯ࢗ଀ۢĂ คѨͧᄃคࢦă˧ጯણᇴ̝ˬ۰ᙯܼĂдি౻ᐸෘ͞ࢬĂ

ܑˣ ᐸෘ̶ژ̝คࢦͧ-ᑕតͧ-คѨͧ

(ε_tx/ε_t18) (N_t18/N_tx) คࢦͧ

(L_x/L₁₈) Pen40/50 Pen60/70 MA I Pen40/50 Pen60/70 MA I 0.78

1.00 1.23 1.45 1.68 1.89 2.11

0.78 1.00 1.22 1.44 1.66 1.89 2.11

0.78 1.00 1.22 1.44 1.67 1.89 2.11

0.32 1.00 2.48 5.30 10.12 17.78 29.34

0.32 1.00 2.47 5.25 9.96 17.37 28.29

0.32 1.00 2.48 5.28 10.08 17.68 28.99

ܑ˝ ֘ᖽ̶ژ̝คࢦͧ-ᑕតͧ-คѨͧ

(ε_cx/ε_c18) (N_c18/N_cx) คࢦͧ

(L_x/L₁₈) Pen40/50 Pen60/70 MA I Pen40/50 Pen60/70 MA I 0.78

1.00 1.23 1.45 1.68 1.89 2.11

0.72 1.00 1.28 1.57 1.86 2.14 2.43

0.82 1.00 1.34 1.60 1.86 2.12 2.38

0.71 1.00 1.29 1.59 1.88 2.18 2.47

0.33 1.00 2.45 5.13 9.48 16.15 25.65

0.33 1.00 2.39 4.85 8.78 14.60 22.80

0.33 1.00 2.45 5.12 9.56 16.34 26.09

30

20

10

0

Pen 40/50-(a) Pen 60/70-(a) MA I-(a) Pen 40/50-(b) Pen 60/70-(b) MA I-(b)

0 0.5 1 1.5 2 2.5 3

(a) cx / c18 (b)Lx /L18

Nc18/Ncx

ဦ 15 คࢦͧ-ᑕតͧ-คѨ̝ͧࢷ㌇ᙯܼဦ-֘ᖽ̶ژ

ˬ۰۞ᙯܼߏԆБ˘࡭۞Ă൒҃คࢦͧ׶ᑕតͧд੅ኢ֘

ᖽ̶ژॡĂ֭ܧјቢّᙯܼĄ

3. ᙷৠགྷშྮ࿰ീ EALF

Ϥ˯˘༼̶ژ̚ĂΞ൴ன̙Т۞ྶࢦٙౄј̝֘ᖽᄃ ᐸෘड़ᑕᐌᘒܦ჌ᙷត̼ĂϺӈคࢦăคѨᄃ˧ጯᇴࣃត

̼̙Ⴝ࠹ТĄώࡁտ୬ͽࣆ็ᅍᙷৠགྷშྮ(back-error propagation neural networkĂBPN)۞͞ёĂ҂ณᇆᜩ EALF ᇆᜩણᇴĂ࿰ീ֘ᖽ׶ি౻ᐸෘEALF ̝јड़Ąώࡁտܼ

ӀϡႾ༛ёጯ௫შྮ̚۞ࣆ็ᅍᙷৠགྷშྮBPNĂٙޙϲ

۞ሀݭໄٙޙϲ۞ሀݭໄهтဦ 16ĂВ̶ࠎ̣࣎ࢍზՎ

ូĂт˭ᄲځĈ

(˘) Ᏼ΍׍΃ّܑ̝ጯ௫९ּĂ૟׎ᖼೱјᏮˢШณүࠎ

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X₁

H₁

Y₁

T1

T₂ Y₂ H₂

H₃₀ X₂

X₃ L_x/L₁₈

N_c18/N_cx

Nt18/Ntx cx/ _c18

tx/ _t18

EALF- rut

EALF- crk

ဦ 16 ᙷৠགྷშྮ BPN ሀёϯຍဦ

შྮ۞Ꮾˢតᇴ(X)Ą

(˟) གྷ࿅ᔳᖟᆸ(H)ᄃᏮ΍ᆸࢍზ΍შྮ۞Ꮾ΍តᇴ(Y)Ą (ˬ) ଂጯ௫९ּ۞ϫᇾᏮ΍តᇴࣃ(T)ᄃҤࢍ̝შྮᏮ΍

តᇴ(Y)ͧྵĂՐ΍ᄱमࣃĄ

(α) ॲፂᄱमࣃࢦາአፋშྮᆸม۞ᝋᇴࣃ(Wij,Vjk)Ą (̣) ࢦኑՎូ(˘)~(α)Ăۡזٙѣጯ௫९ּ̝ᄱमࣃӮࢫ

ז౵ҲĂӈܑϯጯ௫ԆјĄ

ࠎ҂ᇋᙷৠགྷშྮሀݭਕዋϡٺEALF ࠹ᙯણᇴ̝ጯ ௫੊ቚĂЯѩĂώࡁտӀϡܑˣܑ̈́˝̝คࢦͧăᑕតͧ

ᄃคѨͧඈѣᙯ۞ણᇴЕˢ҂ณĂВ56 ௡តᇴ௡Ъ༊јጯ ௫९ּĂͽ˭ֶԔᄲځ̝Ĉ

(˘) คࢦͧ(Lx/L18)Ĉคࢦࠎ౵͹ࢋ۞ᇆᜩЯ৵Ă׎̂̈ᙯ

ܼ඾ྮࢬ৔ᗼ۞඀ޘĄ

(˟) ֘ᖽᑕតͧ(εcx/εc18)Ĉѩણᇴࠎዛࢬ໢ޘࠎ 60ƨॡᘒ ܦࢬᆸ౤ొݬۡᑅᒺᑕត̝˧ጯͧࣃĂѩࣃᙯܼ֘ᖽ

̝ዛࢬᒻड़Ą

(ˬ) ᐸෘᑕតͧ(εtx/εt18)Ĉѩણᇴࠎዛࢬ໢ޘࠎ 25ƨॡᘒܦ ࢬᆸغొͪπૺᑕត̝˧ጯͧࣃĂѩࣃᙯܼᐸෘ̝ዛ ࢬᒻड़Ą

ͽጯ௫தણᇴ η ֽଠטᙷৠགྷ̮Հΐгତܕഇ୕

ࣃĂΞ૟ጯ௫தෛࠎ˘࣎ॡតבᇴĂ఺ᇹ۞ᏴፄΞͽܲᙋ

ႊზڱ۞ќᑦ[17]Ą૟˯ࢗᏮˢតᇴͽᗕѡቢϒ̷ᖼೱሀ ё(tansig)Ꮾˢٙనؠ̝ᔳᖟᆸĂѩᆸϤ 30 ࣎ৠགྷ̮ٙ௡

јĂͽቢّᖼೱבᇴ(purelin)үࠎᏮ΍ሀёĂშྮᏮ΍តᇴ ࠎ֘ᖽ̈́ᐸෘ̶ژ̝คѨͧ(Nc18 /Ncx)ᄃ(Nt18 /Ntx)Ă̶Ҿؠ ཌྷࠎEALF-rut ̈́ EALF-crkĂГᄃϫᇾᏮ΍តᇴࣃ(T)ͧྵĂ

༊ᄱमࣃࢫҌ 0.01 ॡܑϯጯ௫ԆјĄώࡁտགྷྏᄱጯ௫

଀Ăጯ௫தɝ=0.3 ̈́኏ณܼᇴɗ=0.5 ࿰ീड़ڍ౵ָĄ඀ё

ેҖ̝ણᇴనؠтܑ˩ٙЕĄ

གྷϤᙷৠགྷშྮ̝ጯ௫јڍ଀΍Ăז˞ௐ 58 ࣎࢜΃

ೈᒖॡӈќᑦĂѩॡ̝ᄱमࣃࠎ0.00963525 ̏ܧ૱ତܕώ ࡁտࣧА઄ؠ۞ᄱमࣃ0.01Ăтဦ 17 ٙϯĂពϯЧણᇴ(ค ࢦͧăᑕតͧᄃคѨͧ)࠰ѣໂ࠹ᙯّĄώࡁտГซ˘Վͽ

౵ָ̼(optimization)͞ڱĂֹϡ౵̈ᓁπ͞ᄱम៍هĂܧ

ܑ˩ ᙷৠགྷშྮጯ௫ᑫֹϡણᇴᄲځ

ֹϡણᇴ ᄲځ

ᔳᖟᆸৠགྷ̮ᇴ ᄱमࣃ(goal)

࢜΃Ѩᇴ(epochs) ጯ௫தη (lr.) Ꮚณܼᇴα (mc.)

30

༊ѩࣃࢫҌ0.01Ă඀ёӈќᑦ ͽ10,0000 Ѩࠎ࢜΃ೈᒖѨᇴ

0.3 0.5

10²

10¹ 10⁰

10^-1

10^-2

10^-3

Performance is 0.00963525, Goal is 0.01

0 10 20 30 40 50

58 Epochs

Training-blue goal-Black

ဦ 17 ᙷৠགྷშྮ̝ EALF ੊ቚጯ௫።඀

ቢّਫ਼ᕩ͞ёᑢЪ(fitting)ޙϲ EALF ̝࿰ീሀёĄͽᇴጯ ೡࢗĂ઄నٙϡ۞ᇴጯሀݭߏy = t ^λ1Ă׎̚λ1ࠎܧቢّࢷ ጕܼᇴĂt ݋ࠎคࢦٕͧᑕតͧĂy ݋ࠎ EALF ࣃĂᓁπ͞

ᄱमࠎE(λ1) = Σ [y- (t ^λ1)]²Ąࠎ˞ವՐ౵ָሀёĂͽSimplex

˭؂ёຩವГᅃͽ౵̈π͞ڱ׽ؠ λ1ĂԱ΍ E(λ1)۞౵̈

ࣃĂ׎࿰ീ౵ָሀёࠎё(17)Ą

5 . 4

18 5 . 4

18 









=











=

−

t tx x

L crk L

EALF ε

ε (17a)

6 . 3

18 4 . 4

18 









=











=

−

c x cx

L rut L

EALF ε

ε (17b)

Ϥё(17a)Ξ࠻΍дᐸෘ̶ژ̚Ăዛࢬٙצז۞คࢦͧ

㌇Ѩ͞ࢺᇴᄃᑕតͧ㌇Ѩ͞ࢺᇴ࠰ࠎ4.5Ăӈᐌ඾ಏคࢦ۞

ᅍᆧĂᑕតͧ׶คࢦͧᆧΐ۞ిޘߏ˘ᇹ۞ĂՀซ˘Վг ᙋځώࡁտ̝EALF-crk ᄃ઼ܑ݈̣ࢗ̚γጯ۰ Deacon[7]

ᄃRamsamooj ඈˠ[9]ٙଯጱ۞คѨͧăคࢦͧ̈́ᑕត̝ͧ

ጕѨ͞ࢺᇴ(׎઄ؠ࠰ࠎ 4)ߏӚЪ۞ćೱ֏̝Ăዛࢬдٚצ

෹ྶ֘ዃٙயϠ̝ি౻ᑕតͅᑕĂ׎৔ᗼ඀ޘᄃคࢦ̝ೀ

ңᆧΐதߏ࠹༊۞Ą҃ё(17b)̝֘ᖽ̶ژ̚Ăคࢦ̝ͧጕ Ѩ͞ࢺᇴ4.4 ᄃ AI ֘ᖽሀё̝ 4.477 ࠹ܕĂ൒҃ᄃᑕតͧ

̝ጕѨ͞ࢺᇴ3.6 ̙֭࠹ТĂࡁҿܼዛࢬᐌคࢦᆧΐĂᘒ ܦࢬᆸ౤ొݬۡᑅᒺᑕត(ε_c)ᐌ̝ᑅ૜Ӕன๬ّĂᔵ൒ᆧ ΐ۞ిޘົు႙ᔌٺቤ׶ᘦؠĂҭѩॡྮࢬѝ̏৔ᗼĂಉ ε׎ࣧѣ۞ڇચͪ໤Ą၌Ѩ͞ᇆᜩEALF ࠤ̂ĂᓝּᄲځĂ

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ࡶͽώ࠷Бᓑඕ֘ࡗ2 ࢺᇾ໤คࢦ۞෹ྶࢦᔒᑅྮࢬĂֶ

ώࡁտ݋EALF-crk=2^4.5=22.6Ăࡶ઼ֶγጯ۰ Deacon[7]ᄃ Ramsamooj ඈˠ[9]Ă݋ EALF-crk=2⁴= 16Ăम෼ࠎ 41%ព

଀ҲҤć֘ᖽ̶ژ̚Ăֶώࡁտ̝คࢦͧ៍ه݋EALF-rut=

2^4.4=21.1Ăࡶֶᑕតͧ៍ه EALF-rut=2^3.6=12.1Ăम෼ࠎ 43%Ă߇෹ྶࢦ֘ٺ֘ᖽᇆᜩࠤᆐĂ୬னಞ៍ീٕٺ࿪ཝ ሀᑢ̶ژෞҤ෹ྶࢦ̝֘֘ᖽ৔ᗼॡĂᅮ̶Ҿ੫၆คࢦค Ѩᄃ˧ጯ̶ژΐͽტЪ҂ณĄ

Ϥͽ˯̈ඕĂ֘ዃ̝คࢦ၆྽ྮ̝৔ᗼ඀ޘ࠹༊ٺ 80kN(18kip)ᇾ໤ಏคࢦͽ 4.4~4.5 ೀң৺ᇴᆧΐĄֶ˯ࢗ

ဦ1 ΞۢĂΗᓑඕ֘ T4 ࠎώ࠷෹ྶ֘ዃ΃ܑ֘჌ĂϤဦ 6 Ξ࠻΍Ă׎෹ྶதࡗࠎ80%ćࡶֶคࢦ༊ณЯ̄҃֏Ăԧ

઼౵̂ಏคคࢦࢨט(10 ̳ጟ)Ă׎คࢦ༊ณЯ̄ࡗࠎᇾ໤

ಏคࢦ̝ 2.7 ࢺĂ࣐Җዺ֘ዃ෹ྶ 80%ӈ׎ಏคࢦࠎ 18 ጟĂ݋׎คࢦ༊ณЯ̄(၆྽ྮ̝৔ᗼ඀ޘ࠹༊ٺᇾ໤คࢦ

̝ࢺᇴ)ࡗࠎ 38.4 ࢺĄೱ֏̝ಏคࢦࠎ 18 ጟ̝෹ྶ֘ዃ၆

྽ྮ̝৔ᗼ඀ޘࡗࠎಏคคࢦ10 ጟ(ԧ઼౵̂ಏคคࢦࢨ ט)̝ 14.2 ࢺĄ

̣ăඕ! ኢ

ώ͛͹ࢋଣ੅ώ࠷Ι֘෹ྶ˭ĂᐌคࢦᄃคѨᆧΐ֘

ᖽ̈́ᐸෘ͞ࢬ̝˧ጯត̼मளĂซ҃ଣ੅EALF ̝࿰ീј ड़Ăፋநͽ˭ᇴᕇඕኢĈ

1. Ϥ֘ᖽᄃᐸෘ৔ᗼ̝˧ጯ̶ژ̚଀ۢĂд֘ᖽ̝ EALF

ࢍზ̚Ăᐌ඾ಏคࢦᅍᆧĂᑕតͧᆧΐ۞ిޘͧคࢦͧ

ֽ଀ԣĂคࢦͧ׶ᑕត֭ͧܧј˘ؠ۞ᙯܼĄ൒҃Ăࢍ

ზEALF ॡĂߏͽ 80kN(18kip)۞ಏคࢦٕߏ׎ٙጱ࡭

۞ᑕតણᇴүࠎ̶ϓĂٙͽд׽ؠՄफ़ણᇴ۞ଐڶ˭ٙ

ࢍზ΍ֽˬ჌ᘒܦՄफ़۞EALF ۞ᔌ๕ߏ࠹ТĂҭд̙

ТᘒܦՄफ़̝ٺྮࢬᒻड़ĂᐌคѨᆧΐĂ׎யϠ̝˧ጯ Җࠎ݋ѣᐹК඀ޘ̶̝Ą

2. ྻϡᙷৠགྷშྮጯ௫੊ቚ EALF ЧᇆᜩតᇴॡĂϤᏮˢ តᇴࠎคࢦͧ̈́ᐸෘᄃ֘ᖽ࠹၆ᑕ̝ 25ƨă60ƨᑕត

̝ͧඕڍ଀ۢĂEALF ጯ௫९ּड़ڍ։рĂᙋځคࢦă คѨᇴ̈́˧ጯણᇴˬ۰ѣۡତᙯܼĄ

3. Ϥ౵̈ᓁπ͞ᄱम౵ָ̼ٙޙϲ̝ EALF ሀёĂ׎֘ᖽ

̶ژ̝คࢦͧᄃᑕត̝ͧ㌇Ѩ͞ࢺᇴ̙֭࠹ඈĂ̶Ҿࠎ 4.4 ׶ 3.6Ă൒҃คࢦ̝ͧጕѨ͞ࢺᇴ 4.4 ᄃ AI ֘ᖽሀ ё̝4.477 ࠹ܕĂࡁҿܼᘒܦࢬᆸᐌคࢦคѨᆧΐ҃ᑅ

૜Ӕன๬ّĂᑅᒺᑕតᆧΐ۞ిޘు႙ᔌٺቤ׶ᘦؠĂ ߇ᑕត̝ͧጕѨ͞ࢺᇴ่ 3.6Ă൒҃ѩॡྮࢬѝ̏৔

ᗼĂಉε׎ࣧѣ۞ڇચͪ໤ćᐸෘ̶ژ͞ࢬĂคࢦͧ׶

ᑕ ត ͧ ׌ ۰̝㌇ Ѩ ͞ ࢺ ᇴ࠰ඈ ٺ 4.5Ăᄃ઼γጯ۰ Deacon[7]ᄃ Ramsamooj ඈˠ[9]ٙଯጱ۞㌇Ѩ͞ࢺᇴ 4

࠹ତܕĂᄲځዛࢬдٚצ෹ྶ֘ዃٙயϠ̝ি౻৔ᗼ඀

ޘᄃคࢦ̝ೀңᆧΐதߏ࠹༊۞Ą

4. ͽώࡁտޙϲ̝ EALF ሀёෞҤࢦ֘෹ྶĂಏคࢦᆧΐ

Ҍ1.23 ࢺᇾ໤ค 80kN ޢĂٙயϠ۞คѨͧͽܧ׽ؠͧ

ּᆐধᅍᆧĂࡶͽώ࠷Бᓑඕ֘ࡗ2 ࢺᇾ໤คࢦ۞෹ྶ

ࢦᔒᑅྮࢬĂዛࢬᐸෘᄃ֘ᖽ৔ᗼ඀ޘΞਕតјᇾ໤ค ࢦ۞ 21~23 ࢺĂ߇ώ࠷ࢦ֘ుѐคࢦăคѨ௢᎕үϡ

˭Ă෹ྶ৔ᗼ඀ޘΞ֍˘೹ĄЯѩĂ੫၆έ៉гડࡀϮ ࢦݭ̝֘෹ྶᚑࢦયᗟĂᑕৼˢคࢦ༊ณЯ̄ٺ྽ྮఢ ထăనࢍă̈́Ⴞநүѣड़̝გטନ߉Ą

5. д EALF ࢍზ̈́࿰ീĂώࡁտͽಏคݭёࠎ͹ĂΞГซ

˘Վଣ੅кคݭё̝EALFĂᏮˢ׎΁Հк࠹ᙯតᇴซ Җ̶ژĂͽ྿ዛࢬ৔ᗼ࿰ീ̝ԆፋّĄ

௑ཱི৶͔

A Մफ़૱ᇴ L₁₈ ᇾ໤คࢦ

L_x Їຍคࢦ(kip)ćL₁΃ܑಏคĂL₂΃ܑᗕคĂL₃΃ܑ

ˬค

n ૱ᇴĂົᐌ඾ྮԖ۞ݭё̈́⯴ࢬඕၹ჌ᙷ҃ள N₁₈ 18kip(80kN)คࢦүϡ˭̝ྶࢦѨᇴ

N_crk ᐸෘ৔ᗼ̝คࢦѨᇴ

N_cx Їຍคࢦx үϡ˭֘ᖽ৔ᗼ̝ྶࢦѨᇴ N_rut ֘ᖽ৔ᗼ̝ྶࢦѨᇴ

N_tx Їຍคࢦx үϡ˭ᐸෘ৔ᗼ̝คࢦѨᇴ N_x Їຍคࢦx ߉ΐคࢦ۞Ѩᇴ

SN ඕၹᇴ

P_t ౵௣ڇચ޽ᇴࠎG_t۞בᇴ

18

εc 18kip(80kN)คࢦүϡ˭ᘒܦᆸ౤ొᑅᑕត εcx Їຍคࢦ x үϡ˭ᘒܦࢬᆸغొͪπૺᑕត

18

εt 18kip(80kN)คࢦүϡ˭ᘒܦᆸغొૺᑕត εtx Їຍคࢦ x үϡ˭ᘒܦࢬᆸ౤ొݬۡᑅᑕត

ણ҂͛ᚥ

1. Ϲ఼ొ௚ࢍ఍ĂĶϹ఼௚ࢍࢋᜓķĂέΔĂέ៉(1997)Ą 2. Chen, J. S., Development of Load Equivalence Factors for the Acceleration Loading Facility, Report to Federal Highway Administration, McLean, Virginia, USA (1990).

3. ౘޙѠăڒԠጳ׶ᖎֈ൞ĂĶࢦ֘෹ྶ၆έ៉ዛࢬ̝ᇆ ᜩķĂ˿ͪ͢ӀĂௐ˟˩ˣסĂௐ˟ഇĂௐ124-137 ࢱ (2001)Ą

4. Chou, C. P., and Ching, C. P., “Truck Load Distribution and Its Impact on Vehicle Weight Regulations in Taiwan,”

Transportation Research Record, Vol. 1501, pp. 87-94 (1996).

5. Chou, C. P., “Effect of Overloaded Heavy Vehicles on Pavement and Bridge Design,” Transportation Research Record, Vol. 1539, pp. 58-65 (1996).

6. Hibbit, Karlsson and Sorensen, ABAQUS User’s Manual,

(11)

Version 6.1, Pawtucket, USA (2000).

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8. American Association of State Highway and Transporta- tion Office (AASHTO), AASHTO Interim Guide for the Design of Flexible Pavement Structure, Washington, D. C., USA (1972).

9. Ramsamooj, D. V., Majidzadeh, K., and Kauffmann, E.

M., “The Analysis and Deign of the Flexibility of Pavements,” Proceedings, 3th International Conference on the Structural Deign of Asphalt Pavements, Vol. 1, pp.

692-704 (1972).

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33-38 (1976).

11. The Nordic Cooperative Research Project for the Application of the AASHO Road Test Results, “Failure Model and Pavement Design and Rehabilitation Systems Developed and Adapted for Conditions Prevailing in the Nordic Countries,” Volume I, Proceedings, 4th Interna- tional Conference on the Structural Deign of Asphalt Pavements, pp. 903-919, Ann Arbor, Michigan, USA

(1977).

12. Southgate, H. F., and Deen, R. C., “Variations of Fatigue Due to Unevenly Loaded Tridem Groups,” University of Kentucky Research Report UKTRP-84-11 (1984).

13. Asphalt Institute (AI), Thickness Design-Asphalt Pave- ments for Highways and Streets, MS-1, 10th edition, Kentucky, USA (1991).

14. ڒԠጳĂĶᑕϡྋژ͞ڱෞҤᘒܦ஄጖˿̝˧ጯ፟

טķĂ౾̀ኢ͛Ă઼ϲјΑ̂ጯĂέݑ(2003)Ą

15. Diaz, M., “Literature Review on Load Equivalence Factors,” Technical Report, ARE, Inc., Austin, Texas, USA (1998).

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75-82 (1996).

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