Characteristics of Heavy Vehicles Using Expressway Networks Based on Weigh-in-motion Data

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Received February 18, 2013/ revised July 9, 2013/ accepted August 7, 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵ǤͷǤͳ͹͵ͳ ǤǤǤ

WIM ᤮ⴲ㛮Ἲ#ⴲⱧ㬚#ኞ❋ᦂḚ#⻏㇦ᶇ#㡷⛯#⍂⛛

׊ๅࢼȵԳঃָ

Gil, Heungbae*, Kang, Sang Gyu**

Characteristics of Heavy Vehicles Using Expressway Networks Based on Weigh-in-motion Data

ABSTRACT

The design life and durability of the bridges are strongly affected by the Gross Vehicle Weight(GVW) of heavyweight trucks. The Weigh-In-Motion(WIM) systems are typically used to collect information on truck total weight and speed. The statistical analysis of the GVW measured using High Speed WIM systems showed that most of heavy vehicles were from Vehicle Type 7, 10, and 12. The analysis was also carried out to determine goodness of fit with theoretical probability distributions. The normal distribution was shown to best describe the overall distribution of GVW. The top 10% of the GVW appeared to best fit by the Weibull 3 probability distribution.

Key words : Expressway, Live loads, WIM(Weigh-in-motion) system, Probability distribution

Ⅹಾ

Ʊప᮹ԕǍᖒŝᖅĥᙹ໦⠪aᨱᯩᨕݡ⩶⪵ྜྷ₉᪡zᮡᵲ₉ప᮹ⅾᵲపⓍʑ᪡ᇥ⡍✚ᖒᮡⓑᩢ⨆ᮥၙ⊹໑, ⅾᵲప᮹✚ᖒᮡWIM ᜽ᜅ

▽ᨱᕽ᮹⊂ᱶߑᯕ░ෝ⪽ᬊ⦹ᩍ❭ᦦ⦹Łᯩ݅. Łᗮࠥಽᔢᨱᖅ⊹ࡽŁᗮWIM ᜽ᜅ▽ᮥ☖⧕⊂ᱶࡽᵲ₉ప᮹ᇥ⡍ෝᇥᕾ⦽đŝ, ݡᇡᇥ ᮹ᵲ₉పᮡ7᳦, 10᳦, 12᳦⪵ྜྷ₉ᨱᕽၽᔾ⦹ᩡ݅. ᯕॅ⪵ྜྷ₉᮹ᱥℕᱢᯙⅾᵲపᇥ⡍᪡ᔢ᭥ⅾᵲపᇥ⡍ᨱݡ⦽⪶ශᇥ⡍༉ߙᮥ⇵ᱶ⦹

ᩡ݅. ᱥℕᱢᯙⅾᵲపᇥ⡍۵ᱶȽ⪶ශᇥ⡍ᨱɝᱲ⦹۵äᮝಽᇥᕾࡹᨩᮝ໑, ᔢ᭥10% ߑᯕ░۵ɚ⊹ᇥ⡍᮹⦹ӹᯙWeibull 3 ⪶ශᇥ⡍ᨱ

aᰆ׳ᮡᱢ⧊ࠥෝw۵äᮝಽӹ┡ԍ݅.

áᔪᨕ Łᗮࠥಽ, ⪽⦹ᵲ, ⇶ᵲĥ, ⪶ශᇥ⡍

1. ᕽು

ࠥಽෝᯕᬊ⦹۵b᳦₉పॅ᮹ⅾᵲప✚ᖒᮥ❭ᦦ⦹ᩍƱప᮹ᖅĥᙹ໦ᯕӹ᯵᳕ᙹ໦ᵲᨱၽᔾ⧁äᮝಽᩩ⊂ࡹ۵↽ݡ⪽⦹ᵲᮥ

ᩩ⊂⦹۵äᮡᖅĥၰԕ⦹ಆ⠪aᨱᕽᦥᵝᵲ᫵⦹݅. AASHTO LRFD BDS(Bridge Design Specifications)᮹✙౎⦹ᵲᮡ1975֥ᨱ

⋱ӹ݅᮹Ontarioᵝᨱᕽᙹ⧪ࡽ✙౎⦹ᵲ᳑ᔍđŝᨱʑၹᮥࢱŁࠥ⇽ࡹᨩ݅. ᵲ₉పᮝಽ❱݉ࡹ۵10,000ݡ᮹✙౎ྕíෝ᳑ᔍ⦹ᩡᮝ໑, ᯕ᳑ᔍđŝෝ☁ݡಽAASHTO LRFD BDSᨱᕽᱽ᜽⦹Łᯩ۵75֥᮹Ŗᬊᙹ໦࠺ᦩᨱၽᔾ⧁ᙹᯩ۵↽ݡ᮹⪽⦹ᵲ⬉ŝෝࠥ⇽⦹ᩡ݅

(Nowak, 1999). ᵝ⧪⦹۵ ₉ప᮹ ⇶ᵲప, ⅾᵲప ॒ᮥ ᯱ࠺ᱢᮝಽ ⊂ᱶ⧁ ᙹ ᯩ۵ WIM(Weigh-In-Motion) ᜽ᜅ▽ᮥ ☖⧕ ⊂ᱶࡽ

✙౎᮹ᵲప✚ᖒsॅᮥ⪽ᬊ⦹ᩍƱప᮹⪽⦹ᵲĥᙹෝᮁࠥ⦹Łᦩᱥᖒ॒ᮥ❱݉⦹ʑ᭥⦽ᩑǍaḡᗮᱢᮝಽᙹ⧪ࡹᨩ݅. Moses (2001)۵ŖᬊᵲᯙƱప᮹ᦩᱥᖒᮥ⠪a⦹ʑ᭥⦽⦹ᵲĥᙹᅕᱶᨱᕽWIM ᜽ᜅ▽ᮥ☖⧕⊂ᱶࡽ✙౎ᵲపߑᯕ░᮹95႒ᇥ᭥ᙹ(95th

ĵܓėॡ

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Table 1. Vehicle Classes

Vehicle Type Axle Arrangements Description

4 Small Trucks B Trucks on a single frame with two axles. Loading limit: 85kN

5 Medium Trucks A Trucks on a single frame with three axles

6 Medium Trucks B Trucks on a single frame with four axles

7 Medium Trucks C Trucks on a single frame with five axles

8 Large Trucks A Semi-trailer trucks with four axles consisting of two units, one of which is a tractor

9 Large Trucks B Single-trailer trucks with four axles consisting of two units, one of which is a tractor

10 Large Trucks C Semi-trailer trucks with five axles consisting of two units, one of which is a tractor

11 Large Trucks D Single-trailer trucks with five axles consisting of two units, one of which is a tractor

12 Large Trucks E Semi-trailer trucks with six axles consisting of two units, one of which is a tractor Percentile)ෝNowakᯕ⊂ᱶ⦽sॅŝእƱ⠪a⦹ᩡ݅. Sivakumar

॒(2011)ᮡWIM ⊂ᱶߑᯕ░ෝᯕᬊ⦹ᩍAASHTO LRFD BDS ᨱ ᱽ᜽ࡽ⪽⦹ᵲᮥ ᔩ೎í ᱽᱶ⦹Ñӹᙹᱶ⧁ ᙹ ᯩ۵ᔢᖙ⦽

ᱩ₉᪡ ႊჶᮥ ᱽ᜽⦹ᩡ݅.

ǎԕᨱᕽ۵ᝁ഑ࠥʑၹ᮹ࠥಽƱᖅĥʑᵡ(⦽ĥᔢ┽ᖅĥჶ) } ၽᮥ᭥⧕WIM ᜽ᜅ▽⪚ᮡBWIM(Bridge WIM) ᜽ᜅ▽ᮥ☖⧕

⊂ᱶࡽᵲపߑᯕ░ෝ⪽ᬊ⦽äᮝಽᅕŁࡹᨕᯩ݅(Hwang, 2009).

Hwang(2009)ᨱ঑෕໕8}ḡᱱᨱᕽ⊂ᱶࡽ200,740ݡ᮹₉ప

ᵲᨱᕽ ✙౎ ⦹ᵲॅᮥ ᇥญ⦹ᩍ ݉ᯝ₉ప ၰ ᩑ⧪₉పᨱ ᮹⧕

Ʊపᨱᕽၽᔾ⦹۵↽ݡ⦹ᵲ⬉ŝෝĥᔑ⦹ᩡ݅. ₉᳦ᄥಽᵲపᮥ

ᇥᕾ⦽đŝ, 7᳦ᵲ⩶✙౎(5⇶)ŝ10᳦ݡ⩶✙౎ᯕ⠪Ɂᱢᮝಽ

aᰆྕÑᬕäᮝಽᱽ᜽⦹ᩡ݅. ੱ⦽bḡᩎᄥ, ₉᳦ᄥಽ⊂ᱶࡽ

✙౎ᵲపߑᯕ░ᨱᕽ₉᳦ᄥಽᔢ᭥10%᪡20%ෝᯕᬊ⦹ᩍƱప ᨱ ၽᔾ⦹۵ ₉పᨱ ᮹⦽ ↽ݡ ᵲప ⬉ŝෝ ᇥᕾ⦹ᩡ݅. Park

॒(2006)ᮡᕽ⧕ᦩŁᗮࠥಽᔢ᮹ࠥłƱᨱBWIM᜽ᜅ▽ᮥᖅ⊹

⦹ᩍ₉పᵲపᯱഭෝᙹḲ⦹ᩡᮝ໑, ᖅĥ⪽⦹ᵲ༉⩶ŝ⦝ಽ⦹ᵲ

༉⩶ᮥ ᱽᦩ⦹ᩡ݅.

ᅙᩑǍᨱᕽ۵Łᗮࠥಽ᮹ŝᱢ₉పॅᮥ݉ᗮ⦹ʑ᭥⦹ᩍĞ ᇡŁᗮࠥಽ ʡ⃽ ḡᩎ ᔢ⧪ᖁŝ ᵲᇡԕයŁᗮࠥಽ ᖁᔑ ḡᩎ

ᔢ⧪ᖁᨱ ᖅ⊹ࡽ Łᗮ⇶ᵲĥ(High-Speed Weigh-in-motion, HS-WIM) ᜽ᜅ▽ᨱᕽ⊂ᱶࡽߑᯕ░ෝᯕᬊ⦹ᩍ, ₉᳦ᄥ⇶ᵲ ప, ⅾᵲప ၰ ᵲపᇥ⡍ ॒᮹ b᳦ ✚ᖒᮥ ᳑ᔍ⦹ᩡ݅. ʡ⃽

ḡᩎᮡ⠙ࠥ3₉ಽ᮹Łᗮࠥಽᯕ໑ᖁᔑḡᩎᮡ⠙ࠥ2₉ಽ᮹

Łᗮࠥಽᯕ݅. HS- WIM(Kwon and Lee, 2010)ᮡ⦝ᨱ᳑⑝⊁

(Piezo Quartz) ᖝᕽෝ⪽ᬊ⦽Łᗮ⇶ᵲĥಽŁᗮࠥಽᔢ᮹ŝᱢ

₉ప݉ᗮᮥ᭥⦹ᩍᖅ⊹ࡹᨩḡอ, ☖ŝ₉పᨱšಉࡽᵝ᫵ᱶᅕ aĥ⊂ࡹŁᯩ݅. ⊂ᱶࡽᯱഭᵲᨱ۵1/100Ⅹ᮹ᱶၡࠥಽ⊂ᱶ

ࡹ۵☖ŝ᜽e, ᗮࠥ, ₉ᖁ, ₉ࢱeĊ, ⇶Ñ, ᱥℕ₉ప᮹ʙᯕ,

⇶ᵲప(Axle Weight), ᱥℕᵲప(Gross Vehicle Weight, GVW),

⇶ݚ ┡ᯕᨕᙹ ॒ᯕ ⡍⧉ࡹᨕ ᯩ݅. ⊂ᱶࡽ ᱶᅕෝ ᯕᬊ⦹ᩍ

ǎ☁⧕᧲ᇡ᮹Ʊ☖ప᳑ᔍšಉᩩȽ(MLTM, 2009)ᨱ঑ෙ12᳦

₉᳦ᇥඹၰԕᇡᇥඹ⎵ऽᨱ঑ෙᖙᇡᱢᯙ₉᳦ᇥඹࠥᙹ⧪ࡽ

݅. 12᳦᮹ ₉ప ᵲᨱᕽ Table 1ᨱ ᯩ۵ 4᳦ ᯕᔢ᮹ ✙౎ᮥ

Ʊప᮹Ñ࠺ᨱᩢ⨆ᮥၙ⋁ᙹᯩ۵ᵲ₉పᮝಽᇥඹ⦹Łᇥᕾᮥ

ᙹ⧪⦹ᩡ݅.

WIM ᜽ᜅ▽ᮡb᳦⪹Ğᄡᙹᨱၝq⦹ᩍ⊂ᱶߑᯕ░᮹ᱶݚᖒ

ᮥ⪶ᅕ⦹ʑ᭥⧕ᕽ۵ᵝʑᱢᯙáƱᱶŝ᪅₉ᅕᱶᯕ᫵Ǎࡽ݅.

HS-WIM ᜽ᜅ▽᮹áƱᱶᯕᯕ൉ᨕḥḢ⬥ᯙ2011֥11ᬵᵲᙽ ᨱᕽ12ᬵᵲᙽʭḡ⦽ݍ࠺ᦩ⊂ᱶࡽߑᯕ░ෝᯕᬊ⦹ᩍ☖⧪

✙౎᮹ᇥ⡍᪡✚ᖒᮥ⠪a⦹ᩡ݅. ✚⯩2011֥12ᬵ5ᯝᇡ░۵

HS-WIM ᜽ᜅ▽ᨱʑၹ⦽Łᗮࠥಽŝᱢ₉ప݉ᗮ᜽ᜅ▽ᮥᬕᩢ

⦹ʑ᭥⦹ᩍ, ŝᱢ᭥ၹ₉ప᮹ⅾᵲప, ᗮ॒ࠥᮥᱥݍ⦹ʑ᭥⦽

VMS(Variable Message Sign) ⢽⇽ᯕ᜽᯲ࡹᨕⅾᵲప✚ᖒᨱ

ᄡ⪵ ᯩᮥ äᮝಽ ᩩᔢࡽ݅.

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Fig. 1. Daily Truck Traffic Volume at Kimchon HS-WIM Site

Table 2. Filtered Truck Data from Kimchon HS-WIM Site

Vehicle Type Count % of Total

4 41,197 28.9%

5 32,863 23.1%

6 11,963 8.4%

7 24,505 17.2%

8 6,776 4.8%

9 386 0.3%

10 16,940 11.9%

11 987 0.7%

12 6,749 4.7%

Fig. 2. GVW Distribution at Kimchon HS-WIM Site

2. ʡ⃽HS-WIMߑᯕ░ᇥᕾ

2.1 ଵ࣢ധෘ߆ंඑ

ʡ⃽HS-WIM ᜽ᜅ▽ᮡ⠙ࠥ3₉ಽ᮹Łᗮࠥಽᔢ⧪ᖁᨱᖅ⊹

ࡹᨕᯩ݅. ₉ಽᄥ☖⧪పᇥᕾđŝ, ݡᇡᇥ᮹✙౎ᮡ3₉ಽෝ

ᯕᬊ⦹ᩡᮝ໑, ⇵ᬵᯕӹƱ⧪॒ᮥ᭥⧕2₉ಽෝᯕᬊ⦹۵✙౎ࠥ

ᯩ۵äᮝಽ⊂ᱶࡹᨩ݅. ʡ⃽HS-WIM ᜽ᜅ▽ᨱᕽ⊂ᱶࡽ☖ŝ

₉ప᮹ ⊂ᱶᔢ ᪅ඹෝ ᱽÑ⦹Ł ߑᯕ░ෝ ᯝᄥಽ ᱶญ⦽ đŝ, Fig. 1ᨱᱽ᜽ࡽäŝzᯕ⠪Ɂᱢᯙᯝᄥ☖⧪ప(Daily Traffic)ᮡ

15,000ݡᯕᔢᯙäᮝಽ⊂ᱶࡹᨩ݅. ੱ⦽⠪ᯝᨱእ⦹ᩍ⮕ᯝᨱ

ᱥℕƱ☖పᯕ᷾a⦹۵äᮝಽӹ┡ԍ݅. 4᳦⪵ྜྷ₉ᯕᔢ᮹ᱥℕ

⪵ྜྷ₉☖⧪పࠥᔢݚ⯩׳ᦥ⠪ᯝ᮹ᯝᄥ✙౎☖⧪ప(Daily Truck Traffic)ᯕ5,000ݡᯕᔢᮝಽʑಾࡹᨩ݅. ə్ӹᱥℕ₉ప᮹Ʊ☖

పᯕ᷾a⦹۵äŝ۵ၹݡಽ☁᫵ᯝŝᯝ᫵ᯝᨱ۵✙౎☖⧪పᯕ

1,500~3,000ݡ ᙹᵡᮝಽ qᗭ⦹۵ äᮝಽ ӹ┡ԍ݅.

1}ᬵ࠺ᦩ⊂ᱶࡽ142,366ݡ᮹ᱥℕ✙౎ᮥ12᳦₉పᇥඹ

᜽ᜅ▽ᨱ঑௝₉᳦ᄥಽᇥඹ⦽đŝ, Table 2ᨱᯩ۵äŝzᯕ

ӹ┡ԍ݅. ݡᇡᇥ᮹✙౎ᯕእƱᱢᱢᮡᵲపᮥᱢᰍ⦹۵2⇶ᮥ

w۵ᗭ⩶⪵ྜྷᙹᘂᬊ4᳦✙౎(28.9%)ŝ3⇶ᮥw۵ᵲ⩶⪵ྜྷᙹ ᘂᬊ5᳦✙౎(23.1%)ᯙäᮝಽӹ┡ԍ݅. ᵲ⩶᮹⪵ྜྷᙹᘂᬊ

✙౎ᵲᔢݡᱢᮝಽᵲపᮥฯᯕᱢᰍ⦹۵5⇶᮹7᳦ݡ⩶⪵ྜྷ₉a

17.2%ෝǍᖒ⦹۵äᮝಽᇥᕾࡹᨩ݅. ᖙၙ✙౩ᯝ్⩶᜾᮹⪵ྜྷ

₉ᯙ5⇶᮹ 10᳦ ݡ⩶⪵ྜྷ₉᪡6⇶᮹ 12᳦ ݡ⩶⪵ྜྷ₉ࠥbb

11.9%᪡ 4.7%ෝ ᱱᮁ⦹۵ äᮝಽ ӹ┡ԍ݅.

⊂ᱶࡽ4᳦ᯕᔢ✙౎᮹ⅾᵲప(Gross Vehicle Weight)ᮡ↽ᗭ

⦹ᵲ7.0kNᨱᕽ↽Ł⦹ᵲ947.7kNʭḡᄡ⪵⦹ᩡᮝ໑, ⅾᵲప᮹

⯩ᜅ☁əఉᮡFig. 2ᨱᯩ۵äŝzᯕ150kNŝ420kNᮥᵲᝍᮝ ಽᔢݚᙹ✙౎ॅᯕᇥ⡍ࡹᨕᯩ۵ᝮᅪᬑญ⩶ᮝಽӹ┡ԍ݅. ࠥಽ Ʊ☖ჶᨱᕽ⨩ᬊ⦹۵✙౎᮹↽ݡⅾᵲపᯙ392kN(40ton)ᮥⅩŝ

⦹۵ŝᱢ✙౎ࠥᱥℕ✙౎☖ŝݡᙹ᮹22%(31,364ݡ)ᨱݍ⦹۵

äᮝಽ ӹ┡ԍ݅.

2.2 ଵ࣢౑ண߆࣡ฃ

ᯝᄥಽ⊂ᱶࡽ✙౎᮹↽ݡᵲప(Maximum), 95 ႒ᇥ᭥ᙹ(95th Percentiles) ᵲప, ⠪Ɂᵲపᮥᯕᬊ⦹ᩍƱప᮹ԕǍᖒŝᦩᱥᖒᨱ

ᩢ⨆ᮥၙ⊹۵ᵲ₉ప᮹ᵲపᄡ⪵ෝእƱ⦹ᩡ݅. ⅾᵲప᮹95႒ᇥ

᭥ᙹ(Percentile)۵Gindy ॒(2007)ᯕ⊂ᱶࡽ✙౎ᵲప᮹✚ᖒ,

✚⯩Ʊపᖅĥၰᦩᱥᖒᨱᩢ⨆ᮥၙ⊹۵ݡ⢽ᵲ₉ప⦹ᵲᮝಽ

⪽ᬊ⦹ᩡ݅.

Fig. 3ᨱ ᯩ۵ äŝ zᯕ, ✙౎᮹ ↽ݡ ᵲపᮡ ᯝᄥಽ Ⓧí

ᄡ⪵⦹۵äᮝಽӹ┡ԍ݅. ᯕᨱእ⦹ᩍ✙౎᮹⠪Ɂᵲపŝ95႒ᇥ

᭥ᙹᵲపᨱ۵ⓑᄡ⪵aᨧᨩ݅. ə్ӹ2011֥12ᬵ5ᯝᇡ░

HS-WIM ᜽ᜅ▽⊂ᱶᯱഭෝ⪽ᬊ⦽ŝᱢ✙౎ᨱ݉ᗮᨱݡ⦽

VMS(Variable Message Sign) ᱶᅕa⢽⇽ࡽ⬥ᨱ۵ŝᱢ₉పᯕ

HS-WIM ᜽ᜅ▽ᖅ⊹Ǎeᮥ⫭⦝⧉ᨱ঑௝☖⧪✙౎᮹↽ݡ

ⅾᵲప ၰ 95႒ᇥ᭥ᙹ ᵲపᯕ qᗭ⦹۵ äᮝಽ ӹ┡ԍ݅.

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Fig. 3. Daily GVW Statics at Kimchon HS-WIM Site

Fig. 4. GVW Histograms by Vehicle Types for Kimchon HS-WIM Site

Table 3. Gross Vehicle Weight Statistics from Kimchon HS-WIM Site (in KN)

Statistics Vehicle Type

7 10 12

Mean of all trucks 418.6 331.6 397.9 Mean of top 10% trucks 475.3 456.3 514.4 Mean of top 5% trucks 483.8 468.5 553.1

95% Percentile 470.8 451.2 487.2

Maximum of all trucks 626.2 777.0 947.7 Fig. 5. Daily Truck Traffic Volume at Sunsan HS-WIM Site

2.3 ఙஂ࣢౑ண߆൉ন

ʡ⃽HS-WIMᨱᕽ⊂ᱶࡽb₉᳦ᄥⅾᵲపᇥ⡍aFig. 4ᨱ

እƱࡹᨕ ᯩ݅. ✙౎ ☖⧪᮹ ฯᮡ ᇡᇥᮥ ₉ḡ⦹۵ 4᳦ŝ 5᳦

ᵲᗭ⩶ ⪵ྜྷ₉᮹ ⅾᵲపᮡ ݡᇡᇥ ⨩ᬊ ✙౎ ⅾᵲపᯙ 392kN ᯕ⦹ᯙäᮥ᦭ᙹᯩ݅. 6᳦, 7᳦, 10᳦, 11᳦ၰ12᳦ᵲݡ⩶

⪵ྜྷ₉ॅᨱ۵ࠥಽƱ☖ჶᨱᕽ⨩ᬊ⦹۵⨩ᬊⅾᵲపᯙ392kNᮥ

Ⅹŝ⦹۵ᵲ₉పᯕ݅ᙹ᳕ᰍ⦽äᮝಽӹ┡ԍ݅. ✚⯩, 7᳦✙౎ᮡ

☖ŝ⬀ᙹࠥฯŁᵲ₉పࠥฯᮡäᮝಽ⊂ᱶࡹᨩᮝ໑, 10᳦ၰ

12᳦ ✙౎ॅᨱᕽ۵ Ʊప᮹ ᦩᱥᨱ ᩢ⨆ᮥ ၙ⊹۵ ŝᱢ ₉ప᮹

Ⓧʑ᪡እᮉᯕ׳ᮡäᮝಽ⊂ᱶࡹᨩ݅. ⊂ᱶࡽŝᱢ₉పᵲᨱᕽ

↽Łᵲపᮡ12᳦ݡ⩶⪵ྜྷ₉ಽ947.7kNᮥʑಾ⦹ᩡᮝ໑, ᝍ᧝ᨱ

800kN ᱶࠥ᮹ᵲపᮥw۵2ݡ᮹12᳦ݡ⩶⪵ྜྷ₉ॅᯕᩑ⧪⦹ᩍ

☖ŝ⦽ äࠥ 2⫭ӹ ʑಾࡹᨩ݅.

₉᳦ᄥಽ⦹ᵲߑᯕ░ෝᇥᕾ⦽đŝ7᳦, 10᳦, 11᳦, 12᳦

ݡ⩶⪵ྜྷ₉᮹⠪Ɂⅾᵲపᯕ׳ᮡäᮝಽTable 3ᨱᯩ۵äŝ

zᯕᇥᕾࡹᨩ݅. Ʊప᮹ᦩᱥᖒၰԕǍᖒᨱᩢ⨆ᮥၙ⊹۵ᵲ₉ప ᮹✚ᖒᮥ❭ᦦ⦹ʑ᭥⦹ᩍ, ᯕॅ₉᳦᮹ᔢ᭥5%᪡10% ⅾᵲప

ߑᯕ░ෝ⠪Ɂ⦽ⅾᵲపࠥTable 3ᨱ᳑ᔍࡹᨕᯩ݅. ⠪Ɂⅾᵲపᮡ

7᳦ ⪵ྜྷ₉a Ⓧḡอ, ᔢ᭥ 5%᪡ 10%᮹ ⠪Ɂ ⅾᵲపŝ ↽ݡ

ᵲపᮡ 12᳦ ⪵ྜྷ₉ᨱᕽ aᰆ ⓑ äᮝಽ ӹ┡ԍ݅.

3. ᖁᔑHS-WIMߑᯕ░ᇥᕾ

3.1 ଵ࣢֗ധ߆

2₉ಽᯙᖁᔑḡᩎ᮹₉ಽᄥᯕᬊపᮥ᳑ᔍ⦽đŝ, 80% ᱶࠥ᮹

⪵ྜྷ₉۵ᵝ⧪₉ಽᯙ2₉ಽෝᯕᬊ⦹ᩡᮝ໑, ⇵ᬵᯕӹƱ⧪॒ᮥ

᭥⧕⇵ᬵ₉ಽᯙ1₉ಽෝᯕᬊ⦹۵⪵ྜྷ₉۵20% ᱶࠥᯙäᮝಽ

⊂ᱶࡹᨩ݅. ᖁᔑHS-WIM ᜽ᜅ▽ᨱᕽ⊂ᱶࡽᯝᄥ☖⧪ప(Daily Traffic)ŝ 4᳦ ⪵ྜྷ₉ ᯕᔢ᮹ ᯝᄥ✙౎☖ŝݡᙹ(Daily Truck Traffic)۵ Fig. 5᪡ zᯕ ӹ┡ԍ݅. እᱶᔢᱢᯙ ⊂ᱶ ߑᯕ░᪡

ʑʑᯕᔢᮝಽᇡᇥᱢᮝಽอ⊂ᱶᯕᙹ⧪ࡽԁḽෝᱽÑ⦹Łߑᯕ

░ෝᯝᄥಽᱶญ⦹ᩡ݅. Fig. 5ᨱᱽ᜽ࡽäŝzᯕᖁᔑǍeᨱ۵

⠪Ɂᱢᮝಽ20,000ݡᯕᔢ᮹₉పᯕ☖⧪⦹۵äᮝಽӹ┡ԍ݅.

⪵ྜྷ₉(4᳦~12᳦) ☖⧪పࠥᔢݚ⯩׳ᦥᵝᵲᨱ۵Ñ᮹9,000ݡ

ᱶࠥaʑಾࡹᨩ݅. ᵝᵲᨱእ⦹ᩍᵝัᨱᱥℕƱ☖పᯕ᷾a⦹۵

(5)

Table 4. Filtered Truck Data from Sunsan HS-WIM Site

Vehicle Type Count % of Total

4 68,893 33.8%

5 61,010 29.9%

6 14,610 7.2%

7 20,765 10.2%

8 6,406 3.1%

9 898 0.4%

10 23,771 11.7%

11 1,133 0.6%

12 6,459 3.2%

Fig. 6. Gross Vehicle Weight Distribution at Sunsan HS-WIM Site

Fig. 7. Daily GVW Statics at Sunsan HS-WIM Site

Fig. 8. GVW Histograms by Vehicle Types for Sunsan HS-WIM Site äᮝಽӹ┡ԍḡอ, ᱥℕ₉ప᮹Ʊ☖ప᷾a⦹۵äŝ۵ၹݡಽ

ᵝัᨱ۵✙౎᮹☖⧪పᯕ3,000ݡᯕ⦹ᙹᵡᮝಽqᗭ⦹۵äᮝಽ

⊂ᱶࡹᨩ݅.

2᳦ ₉పᇥඹ ᜽ᜅ▽ᮥ ঑௝ ⊂ᱶࡽ 203,945ݡ᮹ ⪵ྜྷ₉ෝ

₉᳦ᄥಽᇥඹ⦽đŝ, Table 4ᨱᯩ۵äŝzᯕӹ┡ԍ݅. ݡᇡᇥ ᮹ ₉పᯕ እƱᱢ ᱢᮡ ᵲపᮥ ᱢᰍ⦹۵ ᵲᗭ⩶ ⪵ྜྷ₉ᯙ 4᳦

(33.8%)ŝ5᳦(29.9%)ᯙäᮝಽӹ┡ԍ݅. ᵲ⩶᮹⪵ྜྷᙹᘂᬊ

✙౎ᵲᔢݡᱢᮝಽᵲపᮥฯᯕᱢᰍ⦹۵5⇶᮹7᳦✙౎ᮡ10.2%

ෝǍᖒ⦹۵äᮝಽᇥᕾࡹᨩ݅. ✙౩ᯝ్⩶᜾᮹ݡ⩶⪵ྜྷ₉ᯙ

5⇶᮹ᖙၙ✙౩ᯝ్(10᳦)᪡6⇶᮹ᖙၙ✙౩ᯝ్(12᳦)ࠥbb

11.7%᪡ 3.2%ᯙ äᮝಽ ⊂ᱶࡹᨩ݅.

⊂ᱶࡽ4᳦ᯕᔢ✙౎᮹ⅾᵲప(Gross Vehicle Weight)ᮡ↽ᗭ

⦹ᵲ7kNᨱᕽ↽Ł⦹ᵲ815kNʭḡᄡ⪵⦹ᩡᮝ໑, ⅾᵲప᮹⯩ᜅ

☁əఉᮡFig. 6ᨱᯩ۵äŝzᯕ150kNŝ420kNᮥᵲᝍᮝಽ

ᔢݚᙹ✙౎ॅᯕᇥ⡍ࡹᨕᯩ۵ᝮᅪᬑญ⩶ᮝಽӹ┡ԍ݅. ŝᱢ₉ ప᮹ʑᵡᯙ392kN(40ton)ᮥⅩŝ⦹۵ŝᱢ✙౎ࠥ13.8%(28,055 ݡ)ᨱ ᔢݚ⦹۵ äᮝಽ ӹ┡ԍ݅.

3.2 ଵ࣢౑ண߆࣡ฃ

⊂ᱶࡽ⪵ྜྷ₉᮹↽ݡᵲపᮡFig. 7ᨱᯩ۵äŝzᯕᯝᄥಽ

ᔢݚ⯩ ᄡ⪵⦹۵ äᮝಽ ӹ┡ԍ݅. ᯕᨱ እ⦹ᩍ ⪵ྜྷ₉᮹ ⠪Ɂ

ᵲపŝ95႒ᇥ᭥ᙹᨱ۵ⓑᄡ⪵aᨧᨩ݅. ᵝัᨱ۵⪵ྜྷ₉᮹☖⧪

పᯕqᗭ⧉ᨱ঑௝↽ݡᵲపŝ⠪Ɂᵲపᯕqᗭ⦹۵äᮝಽࠥ

ӹ┡ԍ݅.

3.3 ఙஂ࣢౑ண߆൉ন

ᖁᔑHS-WIMᨱᕽ⊂ᱶࡽⅾᵲపᇥ⡍ෝb₉᳦ᄥಽእƱ⦽

đŝa Fig. 8ᨱ ᱽ᜽ࡹᨕ ᯩ݅. ⪵ྜྷ₉ ☖⧪ప᮹ ฯᮡ ᇡᇥᮥ

₉ḡ⦹۵ᗭ⩶⪵ྜྷ₉(4᳦)ŝᵲ⩶⪵ྜྷ₉(5᳦)᮹ⅾᵲపᮡݡᇡᇥ

⨩ᬊ✙౎ⅾᵲపᯙ392kN(40ton) ᯕ⦹ᯙäᮥ᦭ᙹᯩ݅. 6᳦, 7᳦, 10᳦, 11᳦ၰ12᳦⪵ྜྷ₉ॅᨱ۵ŝᱢ₉ప݅ᙹ᳕ᰍ⦹۵

äᮝಽӹ┡ԍ݅. ✚⯩, 7᳦✙౎ᮡ☖ŝ⬀ᙹࠥฯŁᵲ₉పእᮉࠥ

׳ᮡäᮝಽ⊂ᱶࡹᨩ݅. 10᳦✙౎ŝ12᳦✙౎ᮡ7᳦✙౎ᨱ

(6)

Table 5. Gross Vehicle Weight Statistics from Sunsan HS-WIM Site (in KN)

Statistics

7 10 12

Mean of all trucks 415.1 326.7 378.8 Mean of top 10% trucks 469.6 439.3 480.0 Mean of top 5% trucks 478.8 447.6 506.0 Maximum of all trucks 573.2 581.4 810.3

(a)

(b)

Fig. 9. GVW of Heavy Trucks for Kimchon HS-WIM Site (a) Normal Probability Paper Plot (b) Gumbel Probability Plot እ⦹ᩍ☖ŝݡᙹ۵ᱢḡอ, Ʊప᮹ᦩᱥᨱᩢ⨆ᮥၙ⊹۵ⅾᵲపᯕ

ⓑ ⪵ྜྷ₉a ฯᮡ äᮝಽ ⊂ᱶࡹᨩ݅. ⊂ᱶࡽ ⪵ྜྷ₉᮹ ⅾᵲప

ᵲᨱᕽ ↽Ł ⅾᵲపᮡ 810.3kN(12᳦)ᮝಽ ʑಾࡹᨩ݅.

7᳦, 10᳦, 12᳦᮹ ᱥℕ ⠪Ɂ ⅾᵲపŝ ᔢ᭥ 5% ၰ 10%᮹

⠪Ɂ ⅾᵲప ၰ ₉᳦ᄥ ↽ݡ ᵲపᯕ Table 5ᨱ እƱࡹᨕ ᯩ݅.

ⅾᵲప᮹⠪Ɂᮡ7᳦⪵ྜྷ₉a12᳦⪵ྜྷ₉ᅕ݅Ⓧḡอ, ᔢ᭥

5%᪡ 10% ⪵ྜྷ₉᮹ ⅾᵲప ⠪Ɂᮡ 12᳦ ⪵ྜྷ₉a ⓑ äᮝಽ

ӹ┡ԍ݅. ᯕäᮡ12᳦⪵ྜྷ₉᮹ᵲ₉పእᮉᯕ׳ʑভྙᯕ݅.

4. ⅾᵲప⪶ශᇥ⡍

Ʊప᮹⪽⦹ᵲĥᙹđᱶ, ԕ⦹ಆ⠪a॒ᨱݡ⦽ʑ᳕᮹ᩑǍᨱ ᕽ۵ᔢ᭥10% ⪚ᮡ20%᮹₉పⅾᵲపᨱᱢ⧊⦽⪶ශᇥ⡍ෝ

ᱢᬊ⦹ᩍ Ŗᬊʑe ᵲ᮹ ↽ݡ ⪽⦹ᵲᮥ ⇵ᱶ⦹Ł ᝁ഑ᖒ ॒ᮥ

ᔑᱶ⦹ᩡ݅. Nowak(1999)ᮡ⋱ӹ݅᮹Ontarioᵝᨱᕽ⊂ᱶࡽᵲ

₉పᮥƱపᨱᰍ⦹⦽⬥, ᯕॅᵲ₉పᨱ᮹⧕ၽᔾ⦹۵༉ູ✙᪡

ᱥ݉ಆᮥᱶȽᇥ⡍ಽŁಅ⦹ᩍƱప᮹Ŗᬊᙹ໦ᵲᨱၽᔾ⧁ᙹ

ᯩ۵↽ݡ⦹ᵲ⬉ŝෝࠥ⇽⦹ᩡ݅. Ghosn ॒(2008, 2010)ᮡWIM

⊂ᱶ₉ప⦹ᵲ᮹ᩢ⨆ᯕᱥℕᱢᮝಽ۵ᱶȽᇥ⡍ᨱᇡ⧊ࡹḡᦫḡ อᔢ᭥5%᮹ߑᯕ░۵ᱶȽᇥ⡍ᨱᱢ⧊⦽äᮝಽŁಅ⦹ᩍ↽ݡ⦹

ᵲ⬉ŝෝᮁࠥ⦹ᩡᮝ໑, b᳦✙౎⦹ᵲᨱ᮹⧕Ʊపᨱၽᔾ⦹۵

༉ູ✙᪡ᱥ݉ಆᇥ⡍᮹↽ݡsॅᯕᱶȽᇥ⡍ෝw۵äᮝಽŁಅ

⦹ᩡ݅. ə్ӹCaprani ॒(2006)ᮡɚ⊹ᇥ⡍ॅᮥ༉ࢱ⡍⧉⦹۵

GEV(Generalized Extreme Value) ᇥ⡍a⦹ᵲᨱ᮹⦽Ʊపᩢ⨆

ᇥ⡍ᨱᱢ⧊⦽äᮝಽᱽ᜽⦹Łᯩ݅. Hwang(2009)ᮡᱶȽᇥ⡍

ᅕ݅۵Type-I ɚ⊹ᇥ⡍(Extreme Value Distribution)ᯙGumbel ᇥ⡍a↽ݡᵲపᇥ⡍ෝ᳡޵ᱶ⪶⦹í༉ᔍ⦹Łᩩ⊂⧁ᙹᯩ۵

äᮝಽᱽ᜽⦹ᩡᮝ໑, ᖅĥ⦹ᵲᮥᮁࠥ⦹۵ߑ⪽ᬊ⦹ᩡ݅. Zhou

॒(2012)ᮡNormal ᇥ⡍, Gumbel ᇥ⡍, GEV ᇥ⡍᪡zᮡ☖ĥ

⪶ශᇥ⡍a ↽ݡ ⦹ᵲ ⬉ŝෝ ᮁࠥ⦹۵ߑ ᯩᨕ ၙ⊹۵ ᩢ⨆ᮥ

እƱ⦹ᩍ, ᱢᬊࡽᇥ⡍ᨱ঑௝↽ݡ⦹ᵲᯕᄡ⦹۵äᮥᅕᩍᵝᨩ݅.

ʡ⃽ŝᖁᔑHS-WIM ᜽ᜅ▽ᨱᕽ⊂ᱶࡽ₉ప᮹ⅾᵲపߑᯕ░

ᨱᱢ⧊⦽⪶ශᇥ⡍༉ߙᮥᖁᱶ⦹ʑ᭥⦹ᩍ, ᵲ₉పእᮉᯕ׳ᮡ

7᳦, 10᳦, 12᳦ ⪵ྜྷ₉పᮥ ݡᔢᮝಽ ☖ĥᇥᕾᮥ ᙹ⧪⦹ᩡ݅.

ᱥℕ ⅾᵲప ၰ ᔢ᭥ 5%, 10%᮹ ⅾᵲప ߑᯕ░᪡ ᯝၹᱢᮝಽ

⪽ᬊࡹ۵ ⪶ශᇥ⡍ᯙ ᱶȽᇥ⡍ ၰ Gumbel ᇥ⡍᪡᮹ ᱢ⧊ࠥෝ

ᬑᖁá☁⦹ᩡ݅. ⊂ᱶࡽⅾᵲప, ⇶ᵲపᨱᱢ⧊⦽⪶ශᇥ⡍༉ߙᮥ

áᱶ⦹Ł, Ŗᬊʑeᵲ᮹↽ݡᵲపᯕӹ↽ݡᵲపᨱ᮹⦽༉ູ✙, ᱥ݉ಆ॒ᮥᩩ⊂⦹ʑ᭥⦹ᩍ⪶ශḡ(Probability Paper)aᯕᬊࡽ

݅. ✙౎ᵲపᇥ⡍aᱶȽᇥ⡍ᯕ໕ᱶȽ⪶ශḡ(Normal Probability Paper)ᨱḢᖁᮝಽӹ┡ӹ᧝⦹໑, ɚ⊹ᇥ⡍ᯙGumbel ᇥ⡍ᨱ

ᱢ⧊⦹໕Gumbel ⪶ශḡ(Gumbel Probability Paper)ᨱḢᖁᮝಽ

ӹ┡ӹ᧝⦽݅. ⪶ශḡᨱᯩᨕᙹ⠪⇶ᮡ⊂ᱶࡽ✙౎᮹ⅾᵲపᯕ

ࡹ໑, ᙹḢ⇶ᮡ⇶ᗭᄡప(Reduced variate)ᮝಽ⪹ᔑ⦹ᩍࠥ᜽⦽

݅. b ᇥ⡍ᄥ ⇶ᗭᄡపᮡ ݅ᮭŝ zᯕ Ǎ⧁ ᙹ ᯩ݅.

Ɣ á ĳ^àÎÞƎß (1)

ᩍʑᕽ, Ɣ = ᱶȽᇥ⡍ ⇶ᗭᄡప

(7)

(a)

(b)

Fig. 10. GVW of Heavy Trucks for Sunsan HS-WIM Site (a) Normal Probability Paper Plot (b) Gumbel Probability Plot

Gross Vehicle Weight (kN)

440 460 480 500 520 540 560 580 600 620 640

Normal Redeced Variate

-4 -3 -2 -1 0 1 2 3 4

Top 10%

Top 5%

(a)

440 460 480 500 520 540 560 580 600 620 640

Gumbel Reduced Variate

-4 -2 0 2 4 6 8 10

Top 10%

Top 5%

(b)

Fig. 11. Distributions fitted to Kimchon HS-WIM Data for Vehicle Type 7 (a) Normal Probability Paper Plot (b) Gumbel Probability Plot

400 500 600 700 800 900 1000

Normal Reduced Variate

-4 -3 -2 -1 0 1 2 3 4

Top 10%

Top 5%

(a)

400 500 600 700 800 900 1000

Gumbel Reduced Variate

-4 -2 0 2 4 6 8

Top 10%

Top 5%

(b)

Fig. 12. Distributions fitted to Kimchon HS-WIM Data for Vehicle Type 12 (a) Normal Probability Paper Plot (b) Gumbel Probability Plot

⇶ᗭᄡపᮥǍ⦹ʑ᭥⦽bb᮹ⅾᵲప⪶ශ,ƎƇ۵n}᮹ⅾᵲప

ߑᯕ░ෝ᪅෥₉ᙽᮝಽᱶญ⦽⬥, Ǝ_Ƈá ƇîÞƌâÎß᜾ᮥᯕᬊ⦹ᩍ

ᔑᱶ⦹ᩡ݅(Castillo ॒, 2005).

b₉᳦ᄥಽ⊂ᱶࡽⅾᵲపᮥᱶȽ⪶ශḡ(Normal Probability Paper)᪡Gumbel ⪶ශḡ(Gumbel Probability Paper)ᨱࠥ᜽⦽

đŝaFigs. 9 and 10ᨱᵝᨕᲙᯩ݅. ࢱ᳦ඹ᮹⪶ශḡᨱࠥ᜽ࡽ

ʡ⃽ၰᖁᔑHS-WIM᮹ᱥℕᵲపᇥ⡍۵Ḣᖁᮝಽӹ┡ӹḥ

ᦫᦹḡอ, ʑ᳕᮹ᩑǍđŝॅŝᮁᔍ⦹íGumbel ᇥ⡍ᅕ݅۵

ᱶȽᇥ⡍ᨱ ᳡ ޵ ᇡ⧊⦹۵ äᮝಽ ӹ┡ԍ݅.

ᔢ᭥ⅾᵲపߑᯕ░᪡ᱶȽᇥ⡍ၰ Gumbelᇥ⡍᪡᮹ᱢ⧊ࠥ

(Goodness of Fit)ෝáᱶ⦹ʑ᭥⦹ᩍ, ᔢ᭥ⅾᵲపߑᯕ░ॅᮥ

ᄥࠥ᮹⪶ශḡᨱࠥ᜽⦹ᩡ݅. ʡ⃽HS-WIMᨱᕽ⊂ᱶ⦽7᳦ŝ

12᳦⪵ྜྷ₉᮹ᔢ᭥5%᪡10%᮹ⅾᵲపߑᯕ░ෝᱶȽ⪶ශḡ᪡

Gumbel ⪶ශḡᨱࠥ᜽⦽đŝaFigs. 11 and Fig. 12ᨱᵝᨕᲙ

ᯩ݅. ₉᳦ᄥⅾᵲప᮹ߑᯕ░ᱱॅಽǍᖒࡽə௹⥥۵⪶ශḡᨱ

šĥᨧᯕᖁ⩶ᖒᮥᅕᯕḡᦫ۵äᮝಽӹ┡ԍ݅. ᖁᔑHS-WIM᮹

ⅾᵲప ߑᯕ░ ࠥ᜽ đŝࠥ ᮁᔍ⦹í ӹ┡ԍ݅. ᯕäᮡ ʑ᳕᮹

ᖅĥʑᵡॅᨱȽᱶࡽ⪽⦹ᵲॅ᮹ ᮁࠥŝᱶᨱᕽaᱶ⦽äŝ۵

(8)

(a)

(b)

Fig. 13. Q-Q Plots of Extreme Value Distributions fitted to Top 10%

of Kimchon HS-WIM Data for Vehicle Type 7 (a) Weibull 3 Distribution (b) Gumbel Distribution

(a)

(b)

of Kimchon HS-WIM Data for Vehicle Type 12 (a) Weibull 3 Distribution (b) Gumbel Distribution

(a)

(b)

of Sunsan HS-WIM Data for Vehicle Type 7 (a) Weibull 3 Distribution (b) Gumbel Distribution

(a)

(b)

of Sunsan HS-WIM Data for Vehicle Type 12 (a) Weibull 3 Distribution (b) Gumbel Distribution

(9)

Table 6. Parameters of Weibull 3 Distribution for HS-WIM Data

HS-WIM Site Vehicle Type Scale Parameter, ķ Shape Parameter, ĸ Location Parameter, ľ

Kimchon 7 0.925 10.87 463.3

12 0.753 34.50 467.6

Sunsan 7 1.008 13.41 456.3

12 0.752 23.09 444.5

ݍญ, ᱶȽᇥ⡍ӹGumbel ᇥ⡍aᱢ⧊⦽⪶ශᇥ⡍༉ߙᯕᦥܭ

äᮥ ᮹ၙ⦽݅.

HS-WIM ⊂ᱶߑᯕ░᮹݅᧲⦽⪶ශᇥ⡍᪡᮹ᱢ⧊ࠥ(Goodness of Fit) á᷾ᮥ ᭥⧕ b᳦ ⪶ශᇥ⡍᮹ ᱢ⧊ࠥ á᷾ ⥥ಽəఉᯙ

ModelRisk(Vose Software, 2007)ෝ⪽ᬊ⦹ᩡ݅. ModelRisk۵⊂ᱶ

ߑᯕ░᮹b᳦⪶ශᇥ⡍ᨱݡ⦽ᱢ⧊ࠥෝSIC(Schwarz Information Criterion), AIC(Akaike Information Criterion), HQIC(Hannan- Quinn Information Criterion) ॒᮹ᱶᅕ⃺ࠥ(Information Criterion)

ෝ ᯕᬊ⦹ᩍđᱶ⦹Ł, ߑᯕ░ᨱᱢ⧊ࠥa׳ᮡᩑᗮ⪶ශᇥ⡍ෝ

ᙽᕽݡಽᱽ᜽⦽݅. ᱶᅕ⃺ࠥᯙSIC, AIC, HQICaaᰆ ᯲ᮡ

sᮥw۵ᩑᗮ⪶ශᇥ⡍a⊂ᱶߑᯕ░᪡᮹ᱢ⧊ࠥa׳ᦥ☖ĥᱢ

✚ᖒᮥaᰆ᯹⢽⩥⧁ᙹᯩ݅. ᱶȽᇥ⡍᪡ɚ⊹ᇥ⡍ᯙGumbel ᇥ⡍(Maximum Extreme Value Distribution), Weibull ᇥ⡍, Weibull 3 ᇥ⡍॒᮹݅᧲⦽ᩑᗮ⪶ශᇥ⡍᮹ᱶᅕ⃺ࠥෝእƱ⦽

đŝ, Weibull 3 ⪶ශᇥ⡍a aᰆ ׳ᮡ ᱢ⧊ࠥෝ w۵ äᮝಽ

ӹ┡ԍ݅. Weibull 3 ⪶ශᇥ⡍۵3-ๅ}ᄡᙹWeibull ᇥ⡍ෝ᮹ၙ

⦹໑, ᯝၹᱢᮝಽᔍᬊࡹ۵ 2-ๅ}ᄡᙹWeibull ᇥ⡍ᨱእ⦹ᩍ

᭥⊹ๅ}ᄡᙹෝ⇵aᱢᮝಽw۵ᇥ⡍ෝ᮹ၙ⦽݅. 3-ๅ}ᄡᙹ

Weibull ᇥ⡍ᯙWeibull 3᮹⪶ශၡࠥ⧉ᙹ, ƄÞƖß۵݅ᮭŝzᯕ

ᱶ᮹ࡽ݅.

ƄÞƖßá ķĸ^àķÞƖ àľß^ķàÎƙ

Ɯƚ_à

Þ

^ćƖ à ľĸ

ß

^ķ^ƛƝƞ ₍₃₎

ᩍʑᕽķ = Ƚ༉ๅ}ᄡᙹ(Scale Parameter), ĸ=⩶ᔢๅ}ᄡᙹ (Shape Parameter), _ľ = ᭥⊹ๅ}ᄡᙹ(Location Parameter)ෝ

bb ᮹ၙ⦽݅.

⊂ᱶࡽߑᯕ░᮹⪶ශᇥ⡍ᱢ⧊ࠥ۵Q-Qࠥ(Quantile-Quantile Plot)᪡P-Pࠥ(Probability-Probability Plot)ෝ☖⧕ᕽࠥ❭ᦦ⧁

ᙹᯩ݅. ᩍʑᕽ۵ᯕುᱢᯙ⪶ශᇥ⡍᮹ᇥ᭥ᙹ᪡ᯕᨱݡ᮲⦹۵

ߑᯕ░ᇥ⡍᮹ᇥ᭥ᙹ(Quantile)ෝᙹ⠪⇶(x⇶)ŝᙹḢ⇶(y⇶)᮹

᳭⢽ಽ⦹ᩍᱱᮥ⁮ᮡQ-Qࠥෝᯕᬊ⦹ᩍ⪶ශᇥ⡍ෝእƱ⦹ᩡ݅.

Castillo ॒(2005)ᨱ঑෕໕Q-Qࠥᨱᕽݡbᖁ(y=x)ᨱߑᯕ░ॅ

ᯕǑḲ⦹ᩍᖁ⩶ᖒᮥaḡ໕ᯕುᱢᯙ⪶ශᇥ⡍ෝ঑෕۵äᮝಽ

Łಅ⦽݅. Figs. 13~16ᨱʡ⃽HS-WIMŝᖁᔑHS-WIMᨱᕽ

⊂ᱶࡽ 7᳦ŝ 12᳦ ✙౎᮹ ᔢ᭥ 10% ⅾᵲప ߑᯕ░ᨱ ݡ⦽

Weibull 3 ⪶ශᇥ⡍᪡Gumbel ⪶ශᇥ⡍᮹Q-Qࠥaᱽ᜽ࡹᨕ

ᯩ݅. Figs. 13~16ᨱእƱࡹᨕᯩ۵Q-Qࠥᨱᕽࠥʑ᳕ᨱᵝಽ

⪽ᬊࡹᨩ޹ Gumbel ⪶ශᇥ⡍ᅕ݅۵ 3}᮹ ๅ}ᄡᙹෝ w۵

Weibull 3 ⪶ශᇥ⡍a᳡޵ᱢ⧊⦽⪶ශᇥ⡍ಽӹ┡ԍ݅. Table 6ᨱʡ⃽HS-WIMŝᖁᔑHS-WIMᨱᕽ⊂ᱶࡽ✙౎⦹ᵲᨱݡ⦽

Weibull 3 ⪶ශᇥ⡍᮹ ๅ} ᄡᙹ sᯕ ᱽ᜽ࡹᨕ ᯩ݅.

5. đು

Ʊప᮹ᖅĥ᪡ᮁḡšญᨱⓑᩢ⨆ᮥၙ⊹۵⪽⦹ᵲ᮹✚ᖒᮥ

❭ᦦ⦹ʑ᭥⦹ᩍ, Łᗮࠥಽᨱᖅ⊹ࡽHS-WIM(High Speed Weigh- in-Motion) ᜽ᜅ▽ᮥᯕᬊ⦹ᩍ⊂ᱶࡽ₉ప᮹ⅾᵲపᇥ⡍ෝ᳑ᔍ

⦹ᩡ݅. ᳑ᔍ đŝ ݅ᮭŝ zᮡ đುᮥ ᨜ᨩ݅.

(1) 2} ḡᩎᨱ ᖅ⊹ࡽ HS-WIM ᜽ᜅ▽ᮡ ☖ŝ᜽e(ᱶၡࠥ:

1/100Ⅹ), ☖ŝᗮࠥ, ᱥℕᵲపၰ⇶ᄥᵲప॒᮹₉పšಉ

ᔢᖙᱶᅕ᮹⊂ᱶᯕa܆⦹໑, 12᳦ᇥඹ᜽ᜅ▽ᨱ঑ෙᱶၡ⦽

₉᳦ᇥඹࠥa܆⦹݅. áƱᱶࡽHS-WIM ᜽ᜅ▽ᮥᯕᬊ⦹ᩍ

⊂ᱶࡽ1}ᬵ࠺ᦩ᮹ⅾᵲపߑᯕ░ෝᯕᬊ⦹ᩍᩑǍaᙹ⧪ࡹ

ᨩ݅.

(2) bḡᩎᨱᕽᵝᵲ᮹✙౎☖⧪పᯕ5,000ݡෝⅩŝ⦹۵äᮝಽ

ӹ┡ԍᮝ໑, ✙౎᮹ⅾᵲప⯩ᜅ☁əఉᮡ150kNŝ420kNᮥ

ᵲᝍᮝಽᔢݚᙹ᮹✙౎ⅾᵲపᯕᇥ⡍⦹۵ᝮᅪᬑญ⩶ᮝಽ

ӹ┡ԍ݅. ə్ӹƱపᨱᩢ⨆ᮥၙ⊹۵ᵲ₉ప᮹ᇥ⡍۵⊂ᱶ ḡᩎᨱ঑௝₉ᯕaᯩ۵äᮝಽӹ┡ԍ݅. ✙౎᮹⨩ᬊ↽ݡᵲ పᯙ392kNᮥⅩŝ⦹۵ŝᱢ✙౎ࠥ10%ᯕᔢᯙäᮝಽӹ┡

ԍᮝ໑, ↽ݡ ᵲపᯕ 948kNᯙ ✙౎ࠥ ⊂ᱶࡹᨩ݅.

(3) ᵲ₉పᮡ7᳦⪵ྜྷ₉, 10᳦⪵ྜྷ₉, 12᳦⪵ྜྷ₉ᨱᕽݡᇡᇥ

ၽᔾ⦹۵äᮝಽ⊂ᱶࡹᨩᮝ໑, ✚⯩7᳦⪵ྜྷ₉᪡12᳦⪵ྜྷ

₉᮹ᵲ₉పእᮉŝ⠪Ɂⅾᵲపᯕ׳ᮡäᮝಽ⊂ᱶࡹᨩ݅.

ੱ⦽Ʊప᮹⪽⦹ᵲ༉⩶ᮁࠥᨱᵝಽ⪽ᬊࡹ۵ᔢ᭥ⅾᵲప᮹

⠪Ɂࠥ ׳ᮡ äᮝಽ ӹ┡ԍ݅.

(4) ᔢ᭥10%᮹ⅾᵲపߑᯕ░᪡ᯕುᱢᯙ⪶ශᇥ⡍ॅŝ᮹ᱢ⧊

(10)

ࠥෝᱶᅕ⃺ࠥ(Information Criterion)᪡Q-Qࠥෝᯕᬊ⦹ᩍ

᳑ᔍ⦽ đŝ, ʑ᳕ᨱ ᵝಽ ⪽ᬊࡹᨩ޹ ᱶȽᇥ⡍ӹ Gumbel

⪶ශᇥ⡍ᅕ݅۵3}᮹ๅ}ᄡᙹෝw۵Weibull 3 ⪶ශᇥ⡍

᮹ ᱢ⧊ࠥa aᰆ ׳ᮡ äᮝಽ ӹ┡ԍ݅.

(5) ᅕ݅ᱶ⪶⦽ᵲ₉ప᮹ⅾᵲపᇥ⡍✚ᖒᮥ❭ᦦ⦹ʑ᭥⧕ᕽ۵

WIMᯕӹHS-WIM ᜽ᜅ▽ᮥᯕᬊ⧕ᰆʑᱢᮝಽ⊂ᱶࡽ✙౎

ⅾᵲప ߑᯕ░ ⪶ᅕ ၰ ᇥᕾᯕ ⦥᫵⦽ äᮝಽ ❱݉ࡽ݅.

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Caprani, C. and O'Brien, E. (2006). “Statistical computation for extreme bridge traffic load effect.” Proceedings of the 8th.

International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, Scotland.

Castillo, E., Hadi, A., Balakrishnan, N. and Sarabia, J. (2005).

Extreme value and related models with applications in engineering and science, John Wiley & Sons, New Jersey, USA.

Ghosn, M. and Sivakumar, B (2010). “Using weigh-in-motion data for modeling maximum live load effects on highway bridges.”

Bridge Maintenance, Safety, Management and Life-Cycle Optimization, Taylor & Francis Group, London, pp. 927-933.

Ghosn, M., Sivakumar, B. and Moses (2008). “Modeling maximum live load effects in highway bridges.” Life-Cycle Civil Engineering, Biondi & Fgangopol, ed., Taylor & Francis Group, London, pp.

335-341.

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