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Journal of the Korea Concrete Institute

J Korea Inst. Struct. Maint. Insp.
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  • Korea Citation Index (KCI)




์›์ „์ฝ˜ํฌ๋ฆฌํŠธ, ๊ท ์—ด ํญ, ์ •์ƒ์ƒํƒœ, ํ™•์‚ฐ๊ณ„์ˆ˜, ์žฌ๋ นํšจ๊ณผ, ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜
Nuclear power plant concrete, Crack width, Steady-state condition, Diffusion coefficient, Age effect, Apparent diffusion coefficient

1. ์„œ ๋ก 

1990๋…„๋Œ€๊นŒ์ง€๋„ ์ฝ˜ํฌ๋ฆฌํŠธ๋Š” ๋ฐ˜์˜๊ตฌ์ ์œผ๋กœ ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ๋Š” ๊ฑด ์„ค์žฌ๋ฃŒ๋กœ ์ธ์‹๋˜์–ด ์™”์œผ๋‚˜, ํ•ด์•ˆ๊ฐ€์— ์‹œ๊ณต๋œ ๊ตฌ์กฐ๋ฌผ์€ ๋งค๋ฆฝ๋œ ์ฒ  ๊ทผ์˜ ๋ถ€์‹์œผ๋กœ ์ธํ•ด ๋งŽ์€ ์„ฑ๋Šฅ์ €ํ•˜๋ฅผ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ๋‹ค(Broomfield, 1997; Song et al., 2006). ์›์ „๊ตฌ์กฐ๋ฌผ์˜ ๊ฒฝ์šฐ ์ง€์†์ ์ธ ๋ƒ‰๊ฐ์ˆ˜์˜ ์œ ์ž…์ด ํ•„์š”ํ•˜๋ฏ€๋กœ ํ•ด์•ˆ๊ฐ€ ๊ทผ์ฒ˜์— ์œ„์น˜ํ•˜๊ฒŒ ๋˜๋Š”๋ฐ, ํ•ด์ˆ˜์— ์ง ์ ‘ ๋…ธ์ถœ์ด ๋˜๋Š” ์ทจ์ˆ˜๊ตฌ ์ด์™ธ์—๋„ ์—ผํ™”๋ฌผ์˜ ๋น„๋ž˜์— ๋”ฐ๋ผ ์›์ „ ๊ฒฉ ๋‚ฉ๊ณ  ๋ฐ ๋ถ€๋Œ€์‹œ์„ค์€ ์—ผํ•ด์— ๋”ฐ๋ฅธ ์ฒ ๊ทผ๋ถ€์‹์˜ ์œ„ํ—˜์ด ์žˆ๋‹ค(Lee and Kwon, 2016; Yang and Moon, 2012).

์›์ „ ๊ตฌ์กฐ๋ฌผ์€ FA(Fly Ash)๋ฅผ ํ˜ผ์ž…ํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ๋ฅผ ๊ธฐ๋ณธ์ ์œผ ๋กœ ์‚ฌ์šฉํ•˜๊ณ  ์žˆ์œผ๋ฉฐ, ACI 304.3R-96, ACI 211.1-91, ACI 301์˜ ๊ธฐ์ค€์„ ๋”ฐ๋ฅธ๋‹ค(ACI 304.3R-96, 1996; ACI 211.1-91, 2009). ์ด ๋Ÿฌํ•œ ๊ธฐ์ค€์—์„œ๋Š” ์‚ฌ์šฉ๋˜๋Š” ๊ฒฐํ•ฉ์žฌ, ํ˜ผํ™”์žฌ, ๊ณจ์žฌ ๋“ฑ์˜ ์‚ฌ์šฉ์žฌ๋ฃŒ ์™€ ๋ฌผ-๊ฒฐํ•ฉ์žฌ ๋น„, ์Šฌ๋Ÿผํ”„ ๋ฐ ๊ณต๊ธฐ๋Ÿ‰ ๋“ฑ์˜ ๋ฐฐํ•ฉ์‚ฌํ•ญ์„ ๊ทœ์ •ํ•˜๊ณ  ์žˆ ๋‹ค. ์›์ „๊ตฌ์กฐ์˜ ๊ฒฉ๋‚ฉ๊ตฌ์กฐ๋Š” ๋ฒฝ์ฒด ๋‹จ๋ฉด์ด ์ˆ˜ m์— ์ด๋ฅด๋Š” ๋งค์Šค์ฝ˜ ํฌ๋ฆฌํŠธ ๊ตฌ์กฐ๋ฌผ๋กœ์„œ ์ดˆ๊ธฐ์žฌ๋ น์—์„œ์˜ ๊ฑด์กฐ์ˆ˜์ถ• ๋ฐ ์ˆ˜ํ™”์—ด์— ๋”ฐ๋ฅธ ๊ท ์—ด์ด ๋ฐœ์ƒํ•˜๊ธฐ ์‰ฌ์šฐ๋ฉฐ(Chung and Lee, 2012; Lee et al., 2016; Song et al., 2001; Chung et al., 2004), ๋ฐœ์ƒ๋œ ๊ท ์—ด์€ ์™ธ๋ถ€ ์—ผํ™” ๋ฌผ ์ด์˜จ์˜ ์˜ํ–ฅ์— ๋”ฐ๋ผ ์—ผํ™”๋ฌผ ์œ ์ž…์„ ๊ฐ€์†ํ™” ์‹œํ‚จ๋‹ค. ์œ ์ž…๋œ ์—ผ ํ™”๋ฌผ ์ด์˜จ์€ ์ฒ ๊ทผ์˜ ๋ถ€์‹์„ ์•ผ๊ธฐํ•˜๊ณ  ์ฒ ๊ทผ์ฃผ์œ„์˜ ํŒฝ์ฐฝ์••์— ์˜ํ•ด ๊ท ์—ด์ด ๋”์šฑ ์ฆ๊ฐ€ํ•˜๋ฉฐ, ์ด๋Š” ํ”ผ๋ณต ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋ฐ•๋ฝ ๋ฐ ๋‚ด๋ ฅ์˜ ์ € ํ•˜๋ฅผ ์•ผ๊ธฐํ•œ๋‹ค(Broomfield, 1997; Song et al., 2006; Chung et al., 2008; Kwon et al., 2009; Yokozeki et al., 1998). ์ฝ˜ํฌ๋ฆฌํŠธ ๋‚ด ๋ถ€๋กœ ์œ ์ž…๋œ ์—ผํ™”๋ฌผ ์ด์˜จ์€ ์žฌ๋ น์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ผ ํ™•์‚ฐ์„ฑ์ด ๊ฐ์†Œ๋œ๋‹ค. ์ด๋Š” ๋ช‡ ๊ฐ€์ง€ ์ด์œ ๊ฐ€ ์žˆ์œผ๋‚˜, ์žฌ๋ น์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ฅธ ๊ณต๊ทน๊ตฌ์กฐ ๊ฐœ์„ ๊ณผ ์ด๋กœ ์ธํ•œ ํ™•์‚ฐ ์ €๊ฐ์„ฑ(Ishida et al., 2009; Maekawa et al., 2003), ์ˆ˜ํ™”๋ฌผ ์ฆ๊ฐ€์— ๋”ฐ๋ฅธ ์ž์œ  ์—ผํ™”๋ฌผ ์ด์˜จ์˜ ํก์ฐฉ๋Ÿ‰ ์ฆ๊ฐ€(Thomas and Bamforth, 1999; Leng et al., 2000), ์œ ์ž…๋œ ์—ผํ™”๋ฌผ ๋†๋„๊ตฌ๋ฐฐ์˜ ์ € ํ•˜(Welty et al., 1989) ๋“ฑ์„ ์ฃผ์›์ธ์œผ๋กœ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋‹ค.

๊ฑด์ „๋ถ€์˜ ์—ผํ™”๋ฌผ ์ด๋™์˜ ์‹œ๊ฐ„์˜์กด์„ฑ ํšจ๊ณผ๋Š” ๋งŽ์€ ์—ฐ๊ตฌ์—์„œ ์ง„ ํ–‰๋˜์–ด ์™”์œผ๋‚˜(Park et al., 2012a; Yang et al., 2017a; Yang et al., 2017b), ๊ท ์—ด๋ถ€์˜ ์‹œ๊ฐ„์˜์กด์„ฑ ํ™•์‚ฐ๊ณ„์ˆ˜์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๋Š” ๋งค์šฐ ํฌ ๋ฐ•ํ•˜๋‹ค. ์ฃผ๋กœ ์ •์ƒ์ƒํƒœ(Steady-state condition)์— ๋Œ€ํ•ด์„œ ๊ท ์—ด ํญ ๋ฐ ๊ท ์—ด ์กฐ๋„(Roughness)๋ฅผ ๊ณ ๋ คํ•œ ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰ ์ค‘์ด์ง€๋งŒ ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๊ฐ์†Œํ•˜๋Š” ๊ท ์—ดํŠน์„ฑ์€ ๊ณ ๋ คํ•˜์ง€ ๋ชปํ•˜๊ณ  ์žˆ๋‹ค(Win et al., 2004; Park et al., 2012b; Gerard and Marchand, 2000; JSCE, 2007).

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” 6000 psi๊ธ‰ ๊ณ ๊ฐ•๋„ ์›์ „ ์ฝ˜ํฌ๋ฆฌํŠธ์— ๊ท ์—ด์„ ์ธ ๊ฐ€ํ•˜์—ฌ ์ •์ƒ์ƒํƒœ์—์„œ์˜ ์—ผํ™”๋ฌผ ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹œํ—˜์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค. ์ด ๋ฅผ ์œ„ํ•ด ์ฝ˜ํฌ๋ฆฌํŠธ๋ฅผ ์žฌ๋ น 56์ผ, 180์ผ, 1๋…„๊นŒ์ง€ ์–‘์ƒํ•˜์˜€์œผ๋ฉฐ, ์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ํ™•์‚ฐ ์ €๊ฐ์„ฑ ๋ฐ ๊ท ์—ด ํญ์˜ ๋ณ€ํ™”์— ๋”ฐ๋ฅธ ํ™•์‚ฐํŠน์„ฑ์„ ๊ฐ™์ด ํ‰๊ฐ€ํ•˜๋„๋ก ํ•œ๋‹ค. ๋˜ํ•œ ์ด‰์ง„ ์‹คํ—˜์ด์™ธ์— ๋™์ผ ๋ฐฐํ•ฉ์„ ๊ฐ€์ง€ ๋Š” ๊ท ์—ด๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ๋ฅผ ๋น„๋ง๋Œ€์— ๋…ธ์ถœ์‹œ์ผฐ์œผ๋ฉฐ, 180์ผ ์žฌ๋ น์˜ ๊ฒ‰ ๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ๊ท ์—ด ํญ๊ณผ ํ•จ๊ป˜ ๋ถ„์„ํ•˜์˜€๋‹ค.

2. ์—ผํ™”๋ฌผ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์‹œ๊ฐ„์˜์กด์„ฑ์— ๋”ฐ๋ฅธ ๊ฑฐ๋™ ํ•ด์„

๊ธฐ์กด์˜ ๋งŽ์€ ์—ฐ๊ตฌ์—์„œ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ๊ฐ์†Œ๋ฅผ ๋ชจ๋ธ๋ง ํ•˜๊ณ  ์žˆ๋Š”๋ฐ, ์ด๋Š” ๊ณต๊ทน๊ตฌ์กฐ์˜ ๊ฐœ์„ ์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์ €๊ฐ์„ ๊ธฐ์ดˆ๋กœ ํ•˜๊ณ  ์žˆ๋‹ค(Song et al., 2005). ์ดˆ๊ธฐ์žฌ๋ น ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฑฐ๋™ ์„ ๊ธฐ๋ฐ˜์œผ๋กœํ•œ Ducom ํ”„๋กœ๊ทธ๋žจ์—์„œ๋Š” ๋‹ค์ƒ์ˆ˜ํ™”๋ณตํ•ฉ ๋ฐœ์—ด๋ชจ๋ธ (MCHM: Multi-Component Hydration Model), ์ˆ˜๋ถ„์ด๋™ ๋ชจ๋ธ (MTM: Moiture Transport Model) ๋“ฑ์—์„œ ์ˆ˜ํ™”๋„์— ๋”ฐ๋ฅธ ๊ณต๊ทน ๊ตฌ์กฐ๋ณ€ํ™”์™€ ์ˆ˜๋ถ„์ด๋™ ๋ณ€ํ™”๊ฐ€ ๋™์‹œ์— ๊ณ ๋ ค๋˜๋ฏ€๋กœ ํ™•์‚ฐ ๋ฐ ์œ ์†์„ ๊ณ ๋ คํ•œ ํ”Œ๋Ÿญ์Šค(Flux)ํ•ญ์—์„œ ์ง์ ‘ ๊ฐ์†Œ๋œ ์—ผํ™”๋ฌผ ์œ ์ž…์„ ๊ณ ๋ คํ•˜ ๊ณ  ์žˆ๋‹ค. ์‹(1)์—์„œ๋Š” Nernst-Einstein Equation์„ ์ง€๋ฐฐ๋ฐฉ์ •์‹์œผ ๋กœ ์‚ฌ์šฉํ•˜๋Š” ๋ชจ๋ธ์— ๋Œ€ํ•œ ์ง€๋ฐฐ๋ฐฉ์ •์‹์„ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ๋‹ค(Ishida et al., 2009; Maekawa et al., 2003).

(1)
ฮฑ i โˆ‚ C c l โˆ‚ t + d i ฯ… ( ฯ• S ฮฉ D c l โˆ‚ C c l โˆ‚ x + q ) + Q c l = 0

์—ฌ๊ธฐ์„œ, Ccl์€ ์—ผํ™”๋ฌผ ์ด์˜จ(mol/l), ฮฑi๋Š” ๋น„์šฉ๋Ÿ‰์œผ๋กœ ฯ•(๊ณต๊ทน ๋ฅ )๊ณผ S(ํฌํ™”๋„)์˜ ํ•จ์ˆ˜, ฮฉ๋Š” ์ž์œ ์ˆ˜ ์ด๋™์„ ๊ณ ๋ คํ•œ ์กฐ๋„๊ณ„์ˆ˜, q ๋Š” ์ˆ˜์••๊ตฌ๋ฐฐ์— ๋”ฐ๋ฅธ ์œ ์†ํ•ญ, Qcl์€ ์ž์œ ์—ผํ™”๋ฌผ ๋†๋„์˜ ์‹œ๊ฐ„์— ๋”ฐ ๋ฅธ ํก์ฐฉ๋Ÿ‰์„ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์ด๋Ÿฌํ•œ ์‹์„ ์‚ฌ์šฉํ•  ๊ฒฝ์šฐ, ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ณต ๊ทน๋ฅ ์˜ ๊ฐ์†Œ์™€ ์ˆ˜๋ถ„์ด๋™์˜ ๊ฐ์†Œ๊ฐ€ ฮฑ, ฯ•, q์— ๊ณ ๋ ค๋˜์–ด ์—ผํ™”๋ฌผ ์ด ๋™์ด ๊ฐ์†Œ๋œ๋‹ค.

์‹คํƒœ์กฐ์‚ฌ ๋˜๋Š” ์žฅ๊ธฐ ์นจ์ง€๋œ ์‹œํŽธ๊ฒฐ๊ณผ๋ฅผ ์ด์šฉํ•œ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„ ์ˆ˜์—์„œ๋Š” ์‹(2)์™€ ๊ฐ™์€ Fick's 2nd Law๋ฅผ ์‚ฌ์šฉํ•˜๊ณ  ์žˆ์œผ๋ฉฐ, ์‹ (3)๊ณผ ๊ฐ™์€ ์‹œ๊ฐ„์˜์กด์„ฑ ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ์‚ฌ์šฉํ•˜๊ณ  ์žˆ๋‹ค(Thomas and Bamforth, 1999; Thomas and Bentz, 2002).

(2)
C ( x , โ€‰ t ) = C 0 ( 1 โˆ’ e r f x 2 D ( t ) โ‹… t )

(3)
D ( t ) = D r e f ( t r e f t ) m

์—ฌ๊ธฐ์„œ, D(t)๋Š” ์‹œ๊ฐ„์˜์กด์„ฑ ํ™•์‚ฐ๊ณ„์ˆ˜(m2/year), t๋Š” ์‹œ๊ฐ„(year), C0๋Š” ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰(kg/m3), C(x, t)๋Š” ๊ฑฐ๋ฆฌ(x)์™€ ์‹œ๊ฐ„(t)์— ๋”ฐ๋ฅธ ์—ผํ™”๋ฌผ๋Ÿ‰์„ ๋‚˜ํƒ€๋‚ธ๋‹ค. Dref์™€ tref๋Š” ๊ธฐ์ค€์‹œ๊ฐ„์—์„œ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜์™€ ๊ธฐ์ค€์‹œ๊ฐ„์„ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ tref์€ 28์ผ์„ ๊ฐ€์ •ํ•œ๋‹ค. ์‹œ๊ฐ„์˜ ์กด์„ฑ ์ง€์ˆ˜(m)์€ ์‹(4)์— ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค(Thomas and Bentz, 2002).

(4)
m = 0.2 + 0.4 ( % F A / 50 โ€‰ + โ€‰ % S G / 70 )

์—ฌ๊ธฐ์„œ, FA, SG๋Š” ๊ฐ๊ฐ ํ”Œ๋ผ์ด์• ์‰ฌ์™€ ์Šฌ๋ž˜๊ทธ์˜ ์น˜ํ™˜์œจ์„ ๋‚˜ ํƒ€๋‚ด๋ฉฐ, ํ”Œ๋ผ์ด์• ์‰ฌ์ธ ๊ฒฝ์šฐ 50%, ์Šฌ๋ž˜๊ทธ์ธ ๊ฒฝ์šฐ 70%๋ฅผ ์ตœ๋Œ€ ๊ฐ’ ์œผ๋กœ ํ•˜๊ณ  ์žˆ๋‹ค.

์—ผํ™”๋ฌผ ํ™•์‚ฐ์˜ ์ฃผ๋œ ๊ธฐ์žฌ๋Š” ๋†๋„์ฐจ์— ์˜ํ•œ ๊ตฌ๋ฐฐ(Gradient)์ด ๋‹ค. ์‹(1)์—์„œ๋Š” ์žฌ๋ น์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์ €๊ฐ์„ ๊ณต๊ทน๋ฅ  ๋˜๋Š” ์ˆ˜ ๋ถ„์ด๋™๊ณผ ๊ฐ™์€ ๋ฌผ๋ฆฌ์ ์ธ ํ•ญ์œผ๋กœ, ์‹(2) ๋ฐ (3)์—์„œ๋Š” ๊ฐ„๋‹จํ•œ ์‹œ๊ฐ„ ์— ๋”ฐ๋ฅธ ์ง€์ˆ˜ํ•จ์†Œ ๋ชจ๋ธ๋กœ ๊ณ ๋ คํ•˜๊ณ  ์žˆ์Œ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค.

3. ์‚ฌ์šฉ์žฌ๋ฃŒ ๋ฐ ์—ผํ™”๋ฌผ ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹คํ—˜๊ณ„ํš

3.1. ์‚ฌ์šฉ์žฌ๋ฃŒ ๋ฐ ๋ฐฐํ•ฉ

์›์ „์šฉ ๋ฐฐํ•ฉ์กฐ๊ฑด์— ๋งž์ถ”์–ด 6000 psi(41 MPa) ๋ฐฐํ•ฉ์„ ์‚ฌ์šฉํ•˜ ์˜€์œผ๋ฉฐ, ์ด๋ฅผ Table 1์— ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๋˜ํ•œ ์‚ฌ์šฉ๋œ ๊ณจ์žฌ ํŠน์„ฑ์€ Table 2์—, ์‚ฌ์šฉ๋œ ์‹œ๋ฉ˜ํŠธ ๋ฐ ํ˜ผํ™”์žฌ์˜ ๋ฌผ๋ฆฌ์ , ํ™”ํ•™์  ํŠน์„ฑ์€ Table 3์— ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค.

Table 1

Mix proportions for nuclear power plant concrete

Grade (psi) Gmax (mm) W/ B S/a W Binder Coarse Agg. Fing Agg.

C FA

6,000 19 40 44.4 162.8 325.5 81.4 938.8 748.9

[i] W/B: Water to binder ratio, S/a: Sand to aggregate, W: Water, C: Cement, FA: Fly ash, Agg.: aggregate

Table 2

Physical properties of aggregate

Items Gmax (mm) Specific gravity (g/cm3) Absorption (%) F.M.
Types

Fine aggregate - 2.58 1.01 2.90
Coarse aggregate 25 2.64 0.82 6.87

[i] F.M.: Fineness Modulus

Table 3

Physical and chemical properties of binder

Items Chemical composition(%) Physical properties

Types SiO2 Al2O3 Fe2O3 CaO MgO SO3 Ig. loss Specific gravity (g/cm3) Blaine (cm2/g)

OPC 21.96 5.27 3.44 63.41 2.13 1.96 0.79 3.16 3,214
FA 55.66 27.76 7.04 2.70 1.14 0.49 4.3 2.19 3,621

3.2. ์••์ถ•๊ฐ•๋„ ์‹คํ—˜

์••์ถ•๊ฐ•๋„ ์‹œํ—˜์€ ์‹œํŽธ์„ 20ยฐC ์˜จ๋„์—์„œ ์ˆ˜์ค‘์–‘์ƒ์„ ํ•˜์˜€์œผ ๋ฉฐ, 56์ผ, 180์ผ, 365์ผ ๊ธฐ๊ฐ„์„ ์–‘์ƒ์กฐ์— ์กด์น˜ํ•œ ๋’ค, KS F 2405 ๊ทœ์ •์— ์˜๊ฑฐํ•˜์—ฌ ์‹œํ—˜์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค.

3.3. ์ •์ƒ์ƒํƒœ ์ด‰์ง„ ์‹คํ—˜ ๋ฐ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ์‹คํ—˜

3.3.1. ๊ท ์—ด์œ ๋„

๊ณ„ํš๋œ ์–‘์ƒ๊ธฐ๊ฐ„ ์ดํ›„ ์—ผํ™”๋ฌผ ํ™•์‚ฐ์‹œํ—˜์„ ํ•˜๊ธฐ ์ „์— ์‹œํŽธ์— ๊ท ์—ด์„ ์œ ๋„ํ•˜์˜€๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ํ‘œ๋ฉด์— ๊ท ์—ด๊ฒŒ์ด์ง€๋ฅผ ๊ท ์—ด์˜ ์ง„์ „ ๋ฐฉํ–ฅ๊ณผ ์ˆ˜์ง์„ ์ด๋ฃจ๋„๋ก ๋ถ€์ฐฉํ•˜์˜€๋‹ค. ์ดํ›„ ํ•˜์ค‘์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ฅธ ๊ท ์—ด ํญ์„ ์ธก์ •ํ•œ ๋’ค ์ œํ•˜(Unloading)์„ ํ•˜์˜€๋‹ค. ์ •ํ™•ํ•œ ๊ท ์—ด ํญ ์„ ๋„์ถœํ•  ์ˆ˜ ์—†์œผ๋ฏ€๋กœ 0.1 mm ๋‹จ์œ„๋กœ ๊ทธ๋ฃนํ•‘ํ•˜๊ธฐ ์œ„ํ•ด ๋‹ค์–‘ํ•œ ๊ท ์—ด์„ ์œ ๋„ํ•˜์˜€๋‹ค. ํ•˜์ค‘ ์ธ๊ฐ€ ์‹œ์—๋Š” ๊ท ์—ด ํญ์ด ์ฆ๊ฐ€ํ•˜๋ฉฐ, ์ œํ•˜ ์‹œ ๊ท ์—ด ํญ์€ ๊ฐ์†Œํ•˜๊ฒŒ ๋˜๋Š”๋ฐ, ์ตœ์ข…์ ์œผ๋กœ ์ œํ•˜์ดํ›„์˜ ๊ท ์—ด ํญ ์„ ์ตœ์ข… ๊ท ์—ด ํญ์œผ๋กœ ์‚ฐ์ •ํ•˜์˜€๋‹ค. Table 4์—์„œ๋Š” ๊ท ์—ด ์ธ๊ฐ€ ์‚ฌ์ง„ ์„ ๋‚˜ํƒ€๋‚ด์—ˆ์œผ๋ฉฐ, ์ง€๋ฆ„ 100 mm, ๋†’์ด 200 mm์ธ ์‹ค๋ฆฐ๋” ์‹œํŽธ์„ 100 mm ๋†’์ด๋กœ ์ปคํŒ…ํ•˜์—ฌ ์‹œํŽธ์— ๊ท ์—ด์„ ์œ ๋„ํ•˜์˜€๋‹ค.

Table 4

Process of the test including mix, crack-inducing, and measuring stage

Mixing and sample preparation JKSMI-21-83_T4-F1.jpg JKSMI-21-83_T4-F2.jpg
Curing and crack inducing JKSMI-21-83_T4-F3.jpg JKSMI-21-83_T4-F4.jpg
Compressive strength and Accelerated diffusion test JKSMI-21-83_T4-F5.jpg JKSMI-21-83_T4-F6.jpg
Exposure to atmospheric condition and AgNO3 titration JKSMI-21-83_T4-F7.jpg JKSMI-21-83_T4-F8.jpg

3.3.2. ์ •์ƒ์ƒํƒœ ์ด‰์ง„์‹คํ—˜

ASTM C 1202์—์„œ ๊ทœ์ •๋œ ์žฅ์น˜์™€ ์‹คํ—˜๋ฐฉ๋ฒ•์„ ์ ์šฉํ•˜์—ฌ ๊ท ์—ด ์„ ๊ฐ€์ง„ ๋””์Šคํฌ ์ฝ˜ํฌ๋ฆฌํŠธ ์‹œํŽธ(D:100 mm, H:100 mm)์„ ์ค€๋น„ ํ•˜์˜€๋‹ค. ์‹œํŽธ์˜ ์ธก๋ฉด์€ ์—ํญ์‹œ๋กœ ์ฝ”ํŒ…ํ•˜์—ฌ 1๋ฐฉํ–ฅ ์—ผํ™”๋ฌผ ์œ ์ž…์„ ์œ ๋„ํ•˜์˜€์œผ๋ฉฐ, ์‹œํŽธ์˜ ์–‘์ชฝ์— ํ™•์‚ฐ์…€์„ ์žฅ์ฐฉํ•˜์˜€๋‹ค. Andrade ๋ฐฉ ๋ฒ•์— ๋”ฐ๋ผ ์–‘๊ทน๋ถ€(anode)์—๋Š” 0.1M NaOH ์šฉ์•ก์„, ์Œ๊ทน๋ถ€ (cathode)์—๋Š” 0.1M NaOH๊ฐ€ ํฌํ•จ๋œ 0.5M์˜ NaCl ์šฉ์•ก์„ ๊ฐ๊ฐ ์ฑ„์šฐ๊ณ  30V์˜ ์ „์••์„ ์†Œ์ •์˜ ์‹œ๊ฐ„๋™์•ˆ ์ธ๊ฐ€ํ•˜์˜€๋‹ค. ์—ผํ™”๋ฌผ ์นจํˆฌ ํ™•์‚ฐ์ด ์ •์ƒ ์ƒํƒœ์— ๋„๋‹ฌํ•  ๋•Œ๊นŒ์ง€ ์ „๋ฅ˜๊ณ„๋ฅผ ํ†ตํ•ด ์ผ์ •ํ•œ ๊ฐ„๊ฒฉ ์œผ๋กœ ํ†ต๊ณผ ์ „๋ฅ˜๋ฅผ ์ธก์ •ํ•˜์˜€์œผ๋ฉฐ, ์ธก์ •๋œ ์ „๋ฅ˜๋Š” ์‹(5)๋ฅผ ์ด์šฉํ•˜ ์—ฌ ์ •์ƒ์ƒํƒœ์˜ ์ด‰์ง„ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ๋„์ถœํ•˜์˜€๋‹ค(Andrade, 1993).

(5)
D e f f = R T n F 2 i t c l ฮ” E L A 1 C c l Z

์—ฌ๊ธฐ์„œ, R์€ ๊ธฐ์ฒด์ƒ์ˆ˜(8.314 J/K โ€ง mol), T๋Š” ์ ˆ๋Œ€์˜จ๋„(K), Z๋Š” ์ด์˜จ๊ฐ€, F ๋Š” Faraday ์ƒ์ˆ˜(9.648ร—104 J/V โ€ง mol), i๋Š” ์‹œํŽธ ํ†ต๊ณผ ์ „๋ฅ˜(Ampere), tcl์€ ์ด๋™ ์ˆ˜, A๋Š” ์‹œํŽธ์˜ ๋‹จ๋ฉด์ (m2), ฮ”E ๋Š” ์ „์••(Volt), L ์€ ์‹œํŽธ์˜ ๋‘๊ป˜(m), Ccl์€ ํ™•์‚ฐ์…€์—์„œ์˜ ์—ผํ™” ๋ฌผ ์ด์˜จ ๋†๋„(mol/l)๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค.

3.3.3. ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹คํ—˜

๋™์ผํ•œ ์›์ „ ๋ฐฐํ•ฉ ์ฝ˜ํฌ๋ฆฌํŠธ์— ๊ท ์—ด์„ ์œ ๋„ํ•œ ๋’ค, ํ•ด์•ˆ๊ฐ€ ๋น„๋ง ๋Œ€์— ๊ท ์—ด๋ฉด์„ ๋…ธ์ถœ์‹œ์ผœ 180์ผ ํ›„ ์ „ ์—ผํ™”๋ฌผ ๋ฐ ์ž์œ ์—ผํ™”๋ฌผ์˜ ํ™• ์‚ฐ์„ฑ์„ ๋ถ„์„ํ•˜์˜€๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ๋ฏธ๋ถ„์‡„ ์‹œ๋ฃŒ๋ฅผ ๋Œ€์ƒ์œผ๋กœ AASHTO T 260์— ๋”ฐ๋ผ ์งˆ์‚ฐ์€ ์šฉ์•ก์„ ์ด์šฉํ•œ ์ „์œ„์ฐจ ์ ์ •๋ฒ•์œผ๋กœ ์‚ฐ ๊ฐ€์šฉ ์„ฑ ์—ผ์†Œ์ด์˜จ๋Ÿ‰์„ ์ธก์ •ํ•œ๋‹ค. ์ด ๋ฐฉ๋ฒ•์€ ๊ธฐ์ง€์˜ ์งˆ์‚ฐ์€(AgNO3) ํ‘œ์ค€์šฉ์•ก์„ ์†Œ๋Ÿ‰์”ฉ ์ฒจ๊ฐ€ํ•˜๋ฉด์„œ ์ด๋•Œ ์„ ํƒ์„ฑ์ด์˜จ์ „๊ทน์˜ ์ „์œ„๋ฅผ ๊ธฐ๋กํ•˜๊ณ  ๋‹น๋Ÿ‰์ ์œผ๋กœ๋ถ€ํ„ฐ ์‹(6)๊ณผ ๊ฐ™์ด ์‹œ๋ฃŒ์˜ ์—ผ์†Œ์ด์˜จ ๋†๋„๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค.

(6)
C l โˆ’ = 3.545 โ€‰ ( N V ) W

์—ฌ๊ธฐ์„œ, Cl-์€ ๋ฏธ๋ถ„์‡„๋œ ์ฝ˜ํฌ๋ฆฌํŠธ ๋ถ„๋ง์‹œ๋ฃŒ ์ค‘์˜ ์—ผ์†Œ์ด์˜จ ๋† ๋„(์ค‘๋Ÿ‰ %), N์€ AgNO3 ํ‘œ์ค€์šฉ์•ก์˜ ๋…ธ๋ฅด๋ง ๋†๋„(N), V์€ ์ข…๋ง ์ ์—์„œ์˜ ์งˆ์‚ฐ์€ ํ‘œ์ค€์šฉ์•ก ์‚ฌ์šฉ๋Ÿ‰(ml), W์€ ๋ฏธ๋ถ„์‡„๋œ ์ฝ˜ํฌ๋ฆฌํŠธ ๋ถ„๋ง์‹œ๋ฃŒ์˜ ์ค‘๋Ÿ‰(g)์„ ๋‚˜ํƒ€๋‚ธ๋‹ค.

Fig. 1์—์„œ๋Š” ์ „์œ„์ฐฉ ์ ์ •๋ฒ•์— ๋”ฐ๋ฅธ ์‹คํ—˜ ์ ˆ์ฐจ๋ฅผ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ ์œผ๋ฉฐ Table 4์—์„œ๋Š” ๋ณธ ์‹คํ—˜์— ๋”ฐ๋ฅธ ์ ˆ์ฐจ๋ฅผ ํ‘œ๋กœ ์ •๋ฆฌํ•˜์˜€๋‹ค.

Fig. 1.

Process of chloride determination by potentiometric titration

JKSMI-21-83_F1.jpg

4. ๊ณ ๊ฐ•๋„ ์›์ „์ฝ˜ํฌ๋ฆฌํŠธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์‹œ๊ฐ„ ๋ฐ ๊ท ์—ดํŠน์„ฑ

4.1. ์••์ถ•๊ฐ•๋„ ํŠน์„ฑ ๋ณ€ํ™”

์žฌ๋ น 56์ผ, 180์ผ, 365์ผ์— ๋Œ€ํ•œ ์••์ถ•๊ฐ•๋„ ๊ฒฐ๊ณผ Fig. 2์— ๋„์‹œ ํ•˜์˜€๋‹ค. ํ‰๊ท ๊ฐ’์€ 56.8 MPa, 59.2 MPa, 61.2 MP๋กœ ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ฐ•๋„๋ฐœํ˜„์„ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค.

Fig. 2.

Compressive strength with ages

JKSMI-21-83_F2.jpg

4.2. ๊ท ์—ด ํญ ๋ฐ ์žฌ๋ น์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ๋ณ€ํ™”

๋ณธ ์ ˆ์—์„œ๋Š” ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ท ์—ด๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜ ๋ณ€ํ™”๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. Fig. 3์—์„œ๋Š” ๊ฐ ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ท ์—ด๋ถ€ ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ๋‚˜ ํƒ€๋‚ด๊ณ  ์žˆ์œผ๋ฉฐ, Fig. 4์—์„œ๋Š” ๊ฐ ์žฌ๋ น์˜ ๊ฑด์ „๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ ํ™•์‚ฐ๊ณ„ ์ˆ˜ ๊ฒฐ๊ณผ์— ๋”ฐ๋ฅธ ๋ณ€ํ™”๋น„์œจ์„ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค.

Fig. 3.

Crack width and enlarged diffusion coefficient

JKSMI-21-83_F3.jpg
Fig. 4.

Crack width and normalized diffusion coefficient

JKSMI-21-83_F4.jpg

์žฌ๋ น 56์ผ ๊ฑด์ „๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ์„œ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” 3.84ร—10-12 m2/sec ๋กœ ํ‰๊ฐ€๋˜์—ˆ๋Š”๋ฐ, ๊ท ์—ด ํญ์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ผ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” ์ฆ๊ฐ€ํ•˜์˜€ ๋‹ค. ๊ท ์—ดํญ 0.4 mmโˆผ0.5 mm์—์„œ๋Š” 2.7๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€๊ณ , 1.0 mm์—์„œ๋Š” 3๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ์žฌ๋ น 180์ผ ๋ฐ 365์ผ ์—์„œ๋„ ๊ฒฝํ–ฅ์„ ๋น„์Šทํ•˜๊ฒŒ ๊ด€์ธก๋˜์—ˆ๋‹ค. 180์ผ ์žฌ๋ น์—์„œ๋Š” ๊ท ์—ดํญ 0.4 mm์ผ ๋•Œ, 1.3๋ฐฐ์˜ ์ฆ๊ฐ€๋ฅผ, 1.0 mm์ผ ๋•Œ, 2.9๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ ๊ฐ€ํ•˜์˜€๋‹ค. ๋˜ํ•œ 365์ผ ์žฌ๋ น์—์„œ๋Š” ์ตœ๋Œ€ 2.7๋ฐฐ ์ •๋„๋กœ ์ฆ๊ฐ€ํ•จ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค. ๋น„์ •์ƒ์ƒํƒœ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹คํ—˜์—์„œ๋Š” ์ดˆ๊ธฐ์— ๊ท ์—ด ํญ ์—์„œ์˜ ์—ผํ™”๋ฌผ ์œ ์ž…์ด ํฌ๊ฒŒ ๋ฐœ์ƒํ•˜์—ฌ 0.4 mm ๊ท ์—ด ํญ์—์„œ 150โˆผ 160๋ฐฐ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜ ์ฆ๊ฐ€๊ฐ€ ํ‰๊ฐ€๋œ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ •์ƒ์ƒํƒœ ์‹คํ—˜์—์„œ ๋Š” ๊ท ์—ด์„ ํฌํ•จํ•œ ์ฝ˜ํฌ๋ฆฌํŠธ ๋‹จ๋ฉด ์ „์ฒด์˜ ์—ผํ™”๋ฌผ ๊ฑฐ๋™์ด ์ธก์ •๋˜ ๋ฏ€๋กœ ๋ณดํ†ต 0.4 mm ๊ท ์—ด ํญ์—์„œ 2.7โˆผ3.0๋ฐฐ์˜ ์ฆ๊ฐ€๋ฅผ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ๋‹ค(Park et al., 2012a). ๋ณธ ์—ฐ๊ตฌ๊ฒฐ๊ณผ์—์„œ๋Š” ์•ฝ๊ฐ„ ๊ฐ์†Œ๋œ 2.5๋ฐฐ ์ˆ˜์ค€์˜ ์ฆ๊ฐ€๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š”๋ฐ, ์žฌ๋ น์˜ ์ฆ๊ฐ€๋กœ ์ธํ•ด ๊ท ์—ด๋ถ€ ํ™•์‚ฐ๊ณ„ ์ˆ˜์˜ ์ฆ๊ฐ€ํญ์ด ๊ฐ์†Œํ•˜์˜€๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ๋˜ํ•œ ๊ธฐ์กด์˜ ๊ท ์—ด์„ ๊ฐ€์ง„ ๋ณดํ†ต๊ฐ•๋„์˜ ์ฝ˜ํฌ๋ฆฌํŠธ์—์„œ์˜ ์ •์ƒ์ƒํƒœ ํ™•์‚ฐ์„ฑ์€ ๊ท ์—ดํญ์— ๋น„์„  ํ˜•์ ์œผ๋กœ ์ฆ๊ฐ€ํ•˜๋Š”๋ฐ, ๊ณ ๊ฐ•๋„ ์›์ „ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฒฝ์šฐ ์„ ํ˜•์— ๊ฐ€ ๊นŒ์šด ๊ฒฐ๊ณผ๊ฐ€ ๋„์ถœ๋˜์—ˆ๋‹ค.

๊ท ์—ด ํญ์ด ์ฆ๊ฐ€ํ• ์ˆ˜๋ก ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” ๋น„์„ ํ˜•์ ์ธ ์ง€์ˆ˜ํ•จ์ˆ˜ ํ˜•ํƒœ ๋กœ ์ฆ๊ฐ€ํ•˜์ง€๋งŒ ๊ท ์—ด ํญ ๋ฐ ์žฌ๋ นํšจ๊ณผ๋ฅผ ๋น„๊ตํ•˜๊ธฐ ์œ„ํ•˜์—ฌ Fig. 3์— ์„œ๋Š” ์„ ํ˜• ํšŒ๊ท€๋ถ„์„์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค. ์‹(7)โˆผ์‹(9)์—์„œ๋Š” ๊ฐ ์žฌ๋ น ์— ๋”ฐ๋ฅธ ๊ท ์—ด๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ํ™•์‚ฐ์ฆ๊ฐ€์— ๋Œ€ํ•œ ํšŒ๊ท€๋ถ„์„ ๊ฒฐ๊ณผ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค.(8)

(7)
Y 56 = 1.823 w + 1 R 2 = 0.700

(8)
Y 180 = 0.919 w + 1 R 2 = 0.725

(9)
Y 365 = 1.2565 w + 1 R 2 = 0.672

์—ฌ๊ธฐ์„œ Yi๋Š” i์žฌ๋ น์—์„œ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜ ์ฆ๊ฐ€์œจ์ด๋ฉฐ, w๋Š” ๊ท ์—ด ํญ (mm)์„ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์žฌ๋ น์ด ์ฆ๊ฐ€ํ• ์ˆ˜๋ก ๊ธฐ์šธ๊ธฐ๊ฐ€ ๊ฐ์†Œํ•˜๋Š” ๊ฒฝํ–ฅ ์ด ๋‚˜ํƒ€๋‚˜๋Š”๋ฐ, ์ด๋Š” ๊ท ์—ด๋ถ€ ํ™•์‚ฐ๊ณ„์ˆ˜ ์—ญ์‹œ ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๊ฐ์†Œํ•˜ ๊ณ  ์žˆ์Œ์„ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ๋‹ค.

4.3. ์žฌ๋ น ๋ฐ ๊ท ์—ดํญ์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜ ๋ณ€ํ™” ์ •๋Ÿ‰ํ™”

๋ณธ ์ ˆ์—์„œ๋Š” ์žฌ๋ น ๋ฐ ๊ท ์—ดํšจ๊ณผ๋ฅผ ํ•˜๋‚˜์˜ ์‹์œผ๋กœ ๋„์ถœํ•˜๊ธฐ ์œ„ ํ•œ ์ •๋Ÿ‰ํ™” ์ž‘์—…์„ ์ˆ˜ํ–‰ํ•˜๋„๋ก ํ•œ๋‹ค. ํ•˜๋‚˜์˜ ์žฌ๋ น์— ๋Œ€ํ•˜์—ฌ ๊ท ์—ด ํญ์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ๋ณ€ํ™”๋Š” ๋น„์„ ํ˜•์œผ๋กœ ์ฆ๊ฐ€ํ•˜๋ฏ€๋กœ ์ง€์ˆ˜ํ•จ์ˆ˜ ๋กœ ๊ฐ๊ฐ์˜ ํ•จ์ˆ˜๋ฅผ ํšŒ๊ท€๋ถ„์„ ํ•˜๋ฉฐ, ๋‹ค์Œ๊ณผ ๊ฐ™์€ ์ ˆ์ฐจ๋ฅผ ๊ฐ€์ง€๋„๋ก ํ•œ๋‹ค.

  • a) ํšŒ๊ท€๋ถ„์„ ์ง€์ˆ˜ํ•จ์ˆ˜ ๋ชจ๋ธ๋ง: ๊ธฐ์กด์˜ ์—ฐ๊ตฌ์— ๋”ฐ๋ผ ๊ท ์—ด๋ถ€์˜ ์ง€์ˆ˜ํ•จ์ˆ˜์˜ ๋น„์„ ํ˜•์  ํšŒ๊ท€๋ถ„์„์„ ์ˆ˜ํ–‰ :

    Y = A ( t ) exp ( E . w ) : โ€‰ w โ€‰ ๊ท ์—ดํญ โ€‰ ( mm )

  • b) 0.0โˆผ0.1 mm, 0.1โˆผ0.2 mm ๋“ฑ 0.1 mm ๊ฐ„๊ฒฉ์œผ๋กœ ๊ฐ ์žฌ๋ น์— ๋”ฐ๋ฅธ ํ‰๊ท  ํ™•์‚ฐ๊ณ„์ˆ˜ ๋„์ถœ(56์ผ, 180์ผ, 365์ผ์˜ ๊ฒฐ๊ณผ์— ๋Œ€ ํ•˜์—ฌ ์ˆ˜ํ–‰)

  • c) ๊ฐ ๊ธฐ์ค€ ๊ฐ’์— ๋Œ€ํ•˜์—ฌ ์ง€์ˆ˜ํ•จ์ˆ˜์‹์„ ํšŒ๊ท€๋ถ„์„ํ•  ๋•Œ, 56์ผ ์žฌ ๋ น์— ๋Œ€ํ•ด์„œ๋Š” 1์˜ ์ ˆํŽธ์„ ๊ฐ€์ ธ์•ผ ํ•˜๊ณ  180์ผ ๋ฐ 365์ผ ์žฌ ๋ น์— ๋Œ€ํ•ด์„œ๋Š” 56์ผ ๊ฒฐ๊ณผ๋ฅผ ๊ธฐ์ค€์œผ๋กœ ํ•œ ๊ฐ์†Œ๋น„๋ฅผ ์ ˆํŽธ์œผ ๋กœ ๊ฐ€์ง€๋„๋ก ํšŒ๊ท€๋ถ„์„.

  • d) a)์—์„œ ์ œ์•ˆ๋œ ์‹์—์„œ A(t)๋Š” ์žฌ๋ น์— ๋Œ€ํ•œ ๊ฐ์†Œ๋ฅผ ๋‚˜ํƒ€๋‚ผ ์ˆ˜ ์žˆ์œผ๋ฉฐ, E๊ฐ’์€ ๊ท ์—ด ํญ์— ๋Œ€ํ•˜์—ฌ ํšŒ๊ท€๋ถ„์„.

  • e) ๊ฐ ํšŒ๊ท€๋ถ„์„ ๊ฒฐ๊ณผ์— ๋Œ€ํ•œ ๊ฐ’์„ ์ด์šฉํ•˜์—ฌ ์žฌ๋ น ๋ฐ ๊ท ์—ด์— ๋Œ€ ํ•œ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๋Š” ์ƒ๊ด€์„ฑ ๋„์ถœ.

Table 5์—์„œ๋Š” ๊ฐ ๊ท ๋“ฑํ™”๋œ ํ™•์‚ฐ๊ณ„์ˆ˜๋น„๋ฅผ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋ฅผ Fig. 5์— ๋„์‹œํ•˜์˜€๋‹ค. ๊ท ์—ดํญ์— ๋Œ€ํ•œ ํ‰๊ท ํ™” ์ž‘์—…์„ ํ•  ๋•Œ, ๊ฐ ๊ท ์—ดํญ์„ 0.1 mm ๋‹จ์œ„๋กœ ๋“ฑ๊ธ‰ํ™” ํ•˜์˜€์œผ๋ฉฐ, ํ‰๊ท ๊ฐ’์˜ 100%๋ฅผ ์ดˆ๊ณผํ•˜๋Š” ํŽธ์ฐจ๋Š” ์ œ์™ธํ•˜์—ฌ ๋‹ค์‹œ ํ‰๊ท ํ™”ํ•˜์˜€๋‹ค.

Table 5

Normalized crack width and diffusion coefficient

Averaged crack width Increasing ratios

56 days 180 days 365 days

0.05 1.000 0.616 0.215
0.15 - 0.625 0.260
0.25 1.141 0.630 0.231
0.35 1.514 - -
0.45 1.263 0.773 0.388
0.55 1.946 0.873 0.432
0.65 1.906 0.778 -
0.75 1.846 0.915 -
0.85 - - -
0.95 - - 0.633
1.05 2.120 - 0.561
1.15 - - 0.670
1.25 - - 1.138
1.35 - 2.946 -
Fig. 5.

Normalized crack width and changes in diffusion coefficient

JKSMI-21-83_F5.jpg

Fig. 5์—์„œ ์•Œ ์ˆ˜ ์žˆ๋“ฏ์ด ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ธฐ์šธ๊ธฐ(A(t))๋Š” ์žฌ๋ น์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ผ 1.000(56์ผ ์žฌ๋ น), 0.616(180์ผ ์žฌ๋ น), 0.215(365์žฌ ๋ น)๋กœ ๊ฐ์†Œํ•˜์˜€์œผ๋ฉฐ, ์ง€์ˆ˜ ๊ฐ’์ธ E๋Š” 0.8366, 0.8419, 1.1116์œผ๋กœ ์ž‘์€ ํญ์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ์ด๋Š” ๊ท ์—ด ํญ์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์ฆ๊ฐ€ ๋น„์œจ์€ ์žฌ๋ น์— ํฌ๊ฒŒ ์˜ํ–ฅ์„ ๋ฐ›์ง€ ์•Š์Œ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค. Fig. 6์—์„œ ๋Š” A(t) ๋ฐ E์˜ ๋ณ€ํ™”๋ฅผ ์žฌ๋ น์— ๋”ฐ๋ผ ๋ถ„์„ํ•˜์˜€๋‹ค.

Fig. 6.

Regression analysis on parameters(A and E)

JKSMI-21-83_F6.jpg

A์— ๋Œ€ํ•ด์„œ๋Š” ๋ช…ํ™•ํ•œ ์„ ํ˜•ํšŒ๊ท€๋ถ„์„ ๊ฒฐ๊ณผ๊ฐ€ ๋„์ถœ๋˜์—ˆ์œผ๋‚˜, E ์— ๋Œ€ํ•ด์„œ๋Š” ์žฌ๋ น์ด 56์ผ์—์„œ 365์ผ๋กœ ์ฆ๊ฐ€ํ•จ์—๋„ ํฐ ์ฐจ์ด๋ฅผ ๋ณด ์ด์ง€ ์•Š์•˜์œผ๋ฏ€๋กœ E๋Š” 0.8366์œผ๋กœ ๋™์ผํ•˜๊ฒŒ ๊ฐ€์ •ํ•˜์˜€๋‹ค.

์ด์ƒ์˜ ๊ฒฐ๊ณผ๋ฅผ ํ•˜๋‚˜์˜ ์‹์œผ๋กœ ์ •๋ฆฌํ•˜๋ฉด ์‹(10)๊ณผ ๊ฐ™์ด ๋‚˜ํƒ€๋‚ผ ์ˆ˜ ์žˆ์œผ๋ฉฐ ์ด ์‹์„ ์ด์šฉํ•œ ๊ฒฐ๊ณผ์™€ ๊ด€๊ณ„ Contour๋ฅผ Fig. 7์— ๋‚˜ํƒ€ ๋‚ด์—ˆ๋‹ค.

Fig. 7.

Regression analysis and contour for the results

JKSMI-21-83_F7.jpg

(10)
Y = [ ( โˆ’ 0.0022 ( t โˆ’ t r e f ) + 1 ] exp [ 0.8366 w ]

์—ฌ๊ธฐ์„œ, Y๋Š” ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์ฆ๊ฐ€ ๋น„๋ฅผ, t๋Š” ์žฌ๋ น, tref๋Š” ๊ธฐ์ค€์žฌ๋ น (56 days)์„ ๋‚˜ํƒ€๋‚ธ๋‹ค.

4.4. ๊ท ์—ด ํญ์˜ ์ฆ๊ฐ€์— ๋”ฐ๋ฅธ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜

3๋…„ ๋™์•ˆ ์ด‰์ง„ ๋ฐ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹œํ—˜์ด ์˜ˆ์ •๋˜์–ด ์žˆ์œผ๋‚˜, ์ œํ•œ๋œ ์ผ์ •์œผ๋กœ ์ธํ•ด ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” 180์ผ ์‹œํ—˜๊ฒฐ๊ณผ๋งŒ ์ œ ์‹œํ•˜๋„๋ก ํ•œ๋‹ค. ์—ผํ™”๋ฌผ ํ”„๋กœํŒŒ์ผ์„ Fick's 2nd Law๋ฅผ ๊ธฐ์ค€์œผ๋กœ ํšŒ๊ท€๋ถ„์„ ํ•  ๊ฒฝ์šฐ ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰ ๋ฐ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ๋„์ถœํ•  ์ˆ˜ ์žˆ๋‹ค. ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์€ ๋…ธ์ถœํ™˜๊ฒฝ์— ๋‹ค๋ฅด๋ฉฐ, ์ผ๋ฐ˜์ ์œผ๋กœ 10โˆผ 12๋…„ ๊นŒ์ง€๋Š” ์„ ํ˜•์ ์œผ๋กœ ๋น ๋ฅด๊ฒŒ ์ฆ๊ฐ€ํ•˜๋ฉฐ ๊ทธ ์ดํ›„๋Š” ํฌ๊ฒŒ ์ฆ๊ฐ€ํ•˜ ์ง€ ์•Š๋Š”๋‹ค(JSCE, 2002). ํ•ด์ˆ˜ ์ค‘์—์„œ๋Š” ๋ณดํ†ต 18.0โˆผ22.0 kg/m3 ์˜ ์ˆ˜์ค€์„ ๊ฐ€์ง€๊ณ  ์žˆ๋‹ค. 180์ผ ๊ฒฝ๊ณผ ์‹œ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” 0.0โˆผ 0.1 mm ๊ท ์—ด ํญ์—์„œ 2.2ร—10-12 m2/sec ์ˆ˜์ค€์˜ ํ™•์‚ฐ๊ณ„์ˆ˜๋ฅผ ๋‚˜ํƒ€ ๋ƒˆ์œผ๋‚˜, 0.4 mm์—์„œ๋Š” 125% ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€์œผ๋ฉฐ, 1.0 mm ๊ท ์—ด ํญ์—์„œ๋Š” 223%๋กœ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค.

์ด‰์ง„ํ™•์‚ฐ๊ณ„์ˆ˜ ์‹คํ—˜๋ณด๋‹ค ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜์—ˆ๋Š” ๋ฐ, ์ด๋Š” ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์ด ๋งค์šฐ ๋‚ฎ์œผ๋ฉฐ ๋น„๋ง๋Œ€ ๋…ธ์ถœํ™˜๊ฒฝ ๊ธฐ๊ฐ„์ด ์งง๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์€ ๊ท ์—ด ์—ฌ๋ถ€์™€ ๊ด€๊ณ„์—†์ด 0.18โˆผ 0.2 kg/m3์˜ ์ˆ˜์ค€์„ ๋‚˜ํƒ€๋‚ฌ๋Š”๋ฐ, ๊ท ์—ด์ด ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์€ ์ž‘์€ ์ˆ˜์ค€์œผ๋กœ ๊ธฐ์กด์˜ ์—ฐ๊ตฌ๊ฒฐ๊ณผ์™€ ๋น„์Šทํ•œ ๊ฒฝํ–ฅ์„ ๋ณด์ด๊ณ  ์žˆ๋‹ค(Kwon et al., 2009). ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์€ ๋น„๋ž˜์ง€์—ญ์˜ ๋…ธ์ถœ๊ธฐ๊ฐ„ ์˜ ์—ฐ์žฅ์— ๋”ฐ๋ผ ์ฆ๊ฐ€ํ•˜๋ฆฌ๋ผ ์˜ˆ์ƒ๋œ๋‹ค. Fig. 8์—์„œ๋Š” ์žฌ๋ น 180์ผ ์˜ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ๊ณ„์ˆ˜ ๋ฐ ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์„ ๋‚˜ํƒ€๋‚ด๊ณ  ์žˆ๋Š”๋ฐ, ๊นŠ์ด 10 mm์— ๋Œ€ํ•œ ๋ถ„๋ง์„ ์ฑ„์ทจํ•˜์˜€์œผ๋ฉฐ, ์ด๋ฅผ ํ‰๊ท ํ•œ ๊ฐ’์„ ์‚ฌ์šฉํ•˜ ์˜€๋‹ค.

Fig. 8.

Apparent diffusion coefficient and surface chloride content

JKSMI-21-83_F8.jpg

5. ๊ฒฐ ๋ก 

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” 6000 psi ๊ธ‰ ์›์ „ ์ฝ˜ํฌ๋ฆฌํŠธ์— ๋Œ€ํ•˜์—ฌ 56์ผ, 180 ์ผ, 1๋…„์˜ ์–‘์ƒ๊ธฐ๊ฐ„์— ๋”ฐ๋ฅธ ์ •์ƒ์ƒํƒœ ์˜๋™์‹คํ—˜์„ ์ˆ˜ํ–‰ํ•˜๊ณ  ๊ท ์—ด ๋ฐ ์žฌ๋ น์ด ํ™•์‚ฐ์„ฑ์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์„ ๋ถ„์„ํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ๋ฅผ ํ†ตํ•ด ๋„์ถœ๋œ ๊ฒฐ๋ก ์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

  • 1) ์žฌ๋ น 56์ผ ๊ฑด์ „๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ์„œ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” 3.84ร—10-12 m2/sec๋กœ ํ‰๊ฐ€๋˜์—ˆ๋Š”๋ฐ, ๊ท ์—ด ํญ 0.4 mmโˆผ0.5 mm์—์„œ๋Š” 2.7๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€๊ณ , 1.0 mm์—์„œ๋Š” 3๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ ๊ฐ€ํ•˜์˜€๋‹ค. 180์ผ ์žฌ๋ น์—์„œ๋Š” ๊ท ์—ด ํญ 0.4 mm์ผ ๋•Œ, 1.3๋ฐฐ์˜ ์ฆ๊ฐ€๋ฅผ, 1.0 mm์ผ ๋•Œ, 2.9๋ฐฐ ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€์œผ๋ฉฐ, 365์ผ ์žฌ๋ น์—์„œ๋Š” ์ตœ๋Œ€ 2.7๋ฐฐ ์ •๋„๋กœ ์ฆ๊ฐ€ํ•จ์„ ์•Œ ์ˆ˜ ์žˆ๋‹ค.

  • 2) ๊ท ์—ด ํญ ๋ฐ ์žฌ๋ น์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜์˜ ์ •๋Ÿ‰ํ™”๋ฅผ ์œ„ํ•˜์—ฌ, ๊ฑด์ „๋ถ€ ์˜ ํ™•์‚ฐ๊ณ„์ˆ˜ ์ €ํ•˜๋Š” ์žฌ๋ น์˜ ํ•จ์ˆ˜๋กœ, ๊ท ์—ด ํญ์— ๋”ฐ๋ฅธ ํ™•์‚ฐ๊ณ„์ˆ˜ ์ฆ๊ฐ€๋Š” ๊ท ์—ด ํญ์˜ ์ง€์ˆ˜ ํ•จ์ˆ˜๋กœ ๊ตฌํ˜„ํ•˜์˜€๋‹ค. ์žฌ๋ น์— ๋”ฐ๋ฅธ ๊ฑด์ „ ๋ถ€์˜ ํ™•์‚ฐ์ €๊ฐ์„ฑ์€ 1๋…„ ๊ฒฝ๊ณผ ์‹œ 21.5% ์ˆ˜์ค€์œผ๋กœ ํฌ๊ฒŒ ๊ฐ์†Œํ•˜ ์˜€์œผ๋‚˜ ๊ท ์—ด ํญ์˜ ์ฆ๊ฐ€์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์€ ์ƒ๋Œ€์ ์œผ๋กœ ๋ฏธ๋น„ํ•˜ ์˜€๋‹ค.

  • 3) 180์ผ ๋™์•ˆ ๋น„๋ง๋Œ€์— ๋…ธ์ถœ๋œ ๊ท ์—ด๋ถ€ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ฒ‰๋ณด๊ธฐ ํ™•์‚ฐ ๊ณ„์ˆ˜๋Š” 0.0โˆผ0.1 mm ๊ท ์—ด ํญ์—์„œ 2.2ร—10-12 m2/sec ์ˆ˜์ค€์œผ๋กœ ํ‰๊ฐ€๋˜์—ˆ๋‹ค. ๊ท ์—ด ํญ์ด 0.4 mm๋กœ ์ฆ๊ฐ€ํ•  ๋•Œ, ํ™•์‚ฐ๊ณ„์ˆ˜๋Š” 125% ์ˆ˜์ค€์œผ๋กœ ์ฆ๊ฐ€ํ•˜์˜€์œผ๋ฉฐ, 1.0 mm ๊ท ์—ด ํญ์—์„œ๋Š” 223% ๋กœ ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ๋˜ํ•œ ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์€ ๋…ธ์ถœ๊ธฐ๊ฐ„์ด ์งง์œผ๋ฉฐ ๋น„ ๋ง๋Œ€์ด๋ฏ€๋กœ 0.18โˆผ0.2 kg/m3์œผ๋กœ ๋งค์šฐ ๋‚ฎ๊ฒŒ ํ‰๊ฐ€๋˜์—ˆ๊ณ , ๊ท  ์—ด ํญ์— ๋”ฐ๋ฅธ ํ‘œ๋ฉด์—ผํ™”๋ฌผ๋Ÿ‰์˜ ๋ณ€ํ™”๋Š” ๊ฑฐ์˜ ์—†์—ˆ๋‹ค.

๊ฐ์‚ฌ์˜ ๊ธ€

๋ณธ ์—ฐ๊ตฌ๋Š” ์‚ฐ์—…ํ†ต์ƒ์ž์›๋ถ€(MOTIE)์™€ ํ•œ๊ตญ์—๋„ˆ์ง€๊ธฐ์ˆ ํ‰๊ฐ€ ์›(KETEP)์˜ ์ง€์›์„ ๋ฐ›์•„ ์ˆ˜ํ–‰ํ•œ ์—ฐ๊ตฌ ๊ณผ์ œ์ž…๋‹ˆ๋‹ค(No. 2015 1520101090).

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