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  1. ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ๊ฑด์ถ•๊ณตํ•™๊ณผ ์„์‚ฌ๊ณผ์ • (Graduate Student, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)
  2. ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ๊ฑด์ถ•๊ณตํ•™๊ณผ ๊ต์ˆ˜ (Professor, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)
  3. ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ๊ฑด์ถ•๊ณตํ•™๊ณผ ์กฐ๊ต์ˆ˜ (Assistant Professor, Department of Architectural Engineering, Kyonggi University, Suwon 16227, Rep. of Korea)



๊ธฐ๋‘ฅ, ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ, ์••์ถ•์—ฐ์„ฑ, ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ, ํšก๋ณด๊ฐ•๊ทผ
column, lightweight aggregate concrete, axial ductility, confined concrete, transverse reinforcement

1. ์„œ ๋ก 

์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ(reinforced concrete, RC) ๊ธฐ๋‘ฅ์€ ์ƒ๋ถ€์—์„œ ์ „๋‹ฌ๋˜๋Š” ์••์ถ•ํ•˜์ค‘๋ฟ๋งŒ ์•„๋‹ˆ๋ผ ์ง€์ง„๊ณผ ๋ฐ”๋žŒ์— ์˜ํ•œ ํšกํ•˜์ค‘์—๋„ ์ €ํ•ญํ•ด์•ผ ํ•ด์„œ ์—ฐ์„ฑํ‰๊ฐ€๊ฐ€ ๋งค์šฐ ์ค‘์š”ํ•œ ์„ค๊ณ„์š”์†Œ์ด๋‹ค(Im 2021). ์ฒ ๊ทผ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ธฐ๋‘ฅ์˜ ์—ฐ์„ฑ์€ ์ฝ˜ํฌ๋ฆฌํŠธ์™€ ์ฃผ์ฒ ๊ทผ์„ ๊ตฌ์†ํ•˜๋Š” ํšก๋ณด๊ฐ•๊ทผ ์–‘($A_{sh}$)์— ์˜ํ•ด ์ค‘์š”ํ•œ ์˜ํ–ฅ์„ ๋ฐ›๋Š”๋‹ค(Kim and Yang 2015). ์ด์— ๋”ฐ๋ผ ACI 318-19(2019)๋Š” ๊ธฐ๋‘ฅ์˜ ์ฝ”์–ด ์ฝ˜ํฌ๋ฆฌํŠธ๋ฅผ ๊ตฌ์†ํ•˜๊ธฐ ์œ„ํ•œ ์ตœ์†Œ ํšก๋ณด๊ฐ•๊ทผ ์–‘($A_{sh(ACI)}$)์„ ์ œ์‹œํ•˜๊ณ  ์žˆ๋‹ค. ์ด๋•Œ $A_{sh(ACI)}$๋Š” ๊ตฌ์†๋œ ์ฝ”์–ด ์ฝ˜ํฌ๋ฆฌํŠธ๋ฅผ ๋ชจ์‚ฌํ•˜๊ธฐ ์œ„ํ•ด์„œ ํšก๋ณด๊ฐ•๊ทผ ๋ฐฐ๊ทผ๊ฐ„๊ฒฉ($s$), ๊ธฐ๋‘ฅ ๋‚ด๋ถ€์˜ ๋‹จ๋ฉด์น˜์ˆ˜, ์ฝ˜ํฌ๋ฆฌํŠธ ์••์ถ•๊ฐ•๋„($f_{ck}$), ํšก๋ณด๊ฐ•๊ทผ ํ•ญ๋ณต๊ฐ•๋„, ๊ธฐ๋‘ฅ ๋‹จ๋ฉด์ , ํšก๋ณด๊ฐ•๊ทผ์˜ ์™ธ๊ณฝ์œผ๋กœ ์‚ฐ์ •๋œ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋‹จ๋ฉด์ ์„ ๊ณ ๋ คํ•˜์˜€๋‹ค. EC 8(CEN 2004)์—์„œ๋„ ์†Œ์š” ์—ฐ์„ฑ๋“ฑ๊ธ‰์— ๋”ฐ๋ฅธ ํšก๋ณด๊ฐ•๊ทผ ์ฒด์ ์ง€์ˆ˜($w_{sh}$)์˜ ํ•˜ํ•œ๊ฐ’์„ ๊ทœ์ •ํ•˜๊ณ  ์žˆ๋‹ค. EC 8(CEN 2004)์—์„œ $w_{sh}$์˜ ํ•˜ํ•œ๊ฐ’์€ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋ฉด์ , ์ž‘์šฉ์ถ•๋ ฅ, ์†Œ์š” ๊ณก๋ฅ ์—ฐ์„ฑ๋น„๋ฅผ ๊ณ ๋ คํ•˜์—ฌ ์‚ฐ์ •๋œ๋‹ค. ํ•˜์ง€๋งŒ ์ด ๊ธฐ์ค€๋“ค์€ ๋ณดํ†ต์ค‘๋Ÿ‰ ์ฝ˜ํฌ๋ฆฌํŠธ(normal-weight concrete, NWC) ๊ธฐ๋‘ฅ์˜ ์‹คํ—˜๊ฒฐ๊ณผ์— ๊ธฐ๋ฐ˜ํ•˜์—ฌ ์ œ์‹œ๋œ ๊ฒฝํ—˜์‹์œผ๋กœ์„œ ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ(lightweight aggregate concrete, LWAC) ๊ธฐ๋‘ฅ์˜ ์—ฐ์„ฑํ™•๋ณด ์ธก๋ฉด์—์„œ๋Š” ์ถ”๊ฐ€์ ์ธ ๊ณ ๋ ค๊ฐ€ ํ•„์š”ํ•˜๋‹ค.

๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ธฐ๋‘ฅ์˜ ์••์ถ• ๋ฐ ํœจ๊ฑฐ๋™์— ๋Œ€ํ•œ ์‹คํ—˜์ž๋ฃŒ๋Š” NWC ๊ธฐ๋‘ฅ์— ๋น„ํ•ด ๋งค์šฐ ๋ถ€์กฑํ•œ ํŽธ์ด๋‹ค. Wei et al.(2020) ๋ฐ Basset and Uzumeri(1986)์€ LWAC ๊ธฐ๋‘ฅ์˜ ์—ฐ์„ฑ์€ $A_{sh}$์ด ์ฆ๊ฐ€ํ• ์ˆ˜๋ก NWC ๊ธฐ๋‘ฅ๊ณผ ๋น„์Šทํ•˜๊ฒŒ ์žˆ์„ ์ˆ˜ ์žˆ์Œ์„ ๋ณด์˜€๋‹ค. ํ•˜์ง€๋งŒ Lim and Ozbakkaloglu(2014)๋Š” LWAC๊ฐ€ NWC์— ๋น„ํ•ด ๊ท ์—ด์ €ํ•ญ์„ฑ์ด ๋‚ฎ๊ณ  ๋” ์ทจ์„ฑํŒŒ๊ดด๋ฅผ ๋ณด์ž„์œผ๋กœ์จ, LWAC ๊ธฐ๋‘ฅ์˜ ์—ฐ์„ฑ์ด ๋™์ผ ์„ค๊ณ„์กฐ๊ฑด์˜ NWC ๊ธฐ๋‘ฅ์— ๋น„ํ•ด ๋‚ฎ์„ ์ˆ˜ ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ $A_{sh}$์ด ๋‚ฎ์„ ๋•Œ LWAC ๊ธฐ๋‘ฅ์˜ ์••์ถ•๊ฑฐ๋™ ๋ฐ ์—ฐ์„ฑํ‰๊ฐ€์— ๋Œ€ํ•œ ๊ธฐ์ดˆ์ž๋ฃŒ๋Š” ์ตœ์†Œ ํšก๋ณด๊ฐ•๊ทผ ์„ค๊ณ„ ๊ด€์ ์—์„œ ์ค‘์š”ํ•˜๋‹ค.

์ค‘์‹ฌ ์ถ•ํ•˜์ค‘์„ ๋ฐ›๋Š” ๊ธฐ๋‘ฅ์—์„œ ๊ตฌ์† ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n}$) ๋ฐ ์—ฐ์„ฑ์„ ๊ฒฐ์ •ํ•˜๋Š” ์ค‘์š”ํ•œ ํŠน์„ฑ์ด๋‹ค(Yang et al. 2021). ์ด์— ๋”ฐ๋ผ ๊ธฐ์กด ์—ฐ๊ตฌ์ž๋“ค์€ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์˜ ์˜ˆ์ธก๋ชจ๋ธ์„ ์ œ์‹œํ•˜๊ณ  ์žˆ๋‹ค. Razvi and Saatcioglu(1999)์€ NWC ๊ธฐ๋‘ฅ์˜ ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘ ์‹คํ—˜์ฒด๋“ค์„ ๊ธฐ๋ฐ˜์œผ๋กœ, ํšก๋ณด๊ฐ•๊ทผ๋Ÿ‰ ๋˜๋Š” ํšก๋ณด๊ฐ•๊ทผ ๋ฐฐ๊ทผํ˜•ํƒœ์— ๋”ฐ๋ฅธ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์˜ ๋ชจ๋ธ์„ ์ œ์‹œํ•˜์˜€๋‹ค. ์ด ๋ชจ๋ธ์€ ์ฝ”์–ด ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ตฌ์†๋ฉด์ ๊ณผ ๊ด€๋ จ๋œ ํ•จ์ˆ˜ ๋ฟ๋งŒ ์•„๋‹ˆ๋ผ ๋“ฑ๊ฐ€ ํšก๊ตฌ์†์••์„ ๊ณ ๋ คํ•˜๊ณ  ์žˆ๋‹ค. ํ•˜์ง€๋งŒ, Razvi and Saatcioglu(1999)์€ NWC ๊ธฐ๋‘ฅ์˜ ์‹คํ—˜๊ฒฐ๊ณผ๋งŒ์œผ๋กœ ๊ตฌ์†ํšจ๊ณผ๋ฅผ ํ‰๊ฐ€ํ•˜๊ณ  ์žˆ์–ด LWAC์˜ ์ตœ๋Œ€์‘๋ ฅ ์ดํ›„์˜ ์ทจ์„ฑ์ ์ธ ๊ฒฝํ–ฅ์„ ๋ฐ˜์˜ํ•  ์ˆ˜ ์—†๋‹ค. ์ด์— ๋ฐ˜ํ•ด Yang et al.(2021)๋Š” ํšก๋ณด๊ฐ•๊ทผ์˜ ์ฒด์ ์ง€์ˆ˜์™€ ํ•จ๊ป˜ ์žฌ๋ฃŒ์  ํŠน์„ฑ(๊ณจ์žฌ์ง๊ฒฝ๊ณผ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋‹จ์œ„์šฉ์  ์งˆ๋Ÿ‰($\rho_{c}$))์˜ ์˜ํ–ฅ์„ ๋ฐ˜์˜ํ•  ์ˆ˜ ์žˆ๋Š” ์ทจ์„ฑ๋„์˜ ๊ฐœ๋…์„ ๋„์ž…ํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ Yang et al.(2021)์€ ์ทจ์„ฑ๋„์˜ ๊ฐœ๋…์ด ๋„์ž…๋œ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๋ชจ๋ธ์ด NWC๋ณด๋‹ค ๋‚ฎ์•„์ง€๋Š” LWAC์˜ ๊ตฌ์†ํšจ๊ณผ๋ฅผ ์ž˜ ๋ฐ˜์˜ํ•˜๊ณ  ์žˆ์Œ์„ ๋ณด์˜€๋‹ค.

์ด ์—ฐ๊ตฌ์˜ ๋ชฉ์ ์€ LWAC ๊ธฐ๋‘ฅ์˜ ์••์ถ•์—ฐ์„ฑ์— ๋Œ€ํ•œ ์„ค๊ณ„๊ธฐ์ค€์˜ ์ตœ์†Œ $A_{sh}$์˜ ์•ˆ์ „์„ฑ์„ ํ‰๊ฐ€ํ•˜๋Š” ๊ฒƒ์ด๋‹ค. ๊ธฐ๋‘ฅ ์‹คํ—˜์ฒด๋Š” LWAC์™€ NWC๋กœ ๊ตฌ๋ถ„ํ•˜๊ณ  $A_{sh}$์€ $A_{sh(ACI)}$์˜ 1.0๋ฐฐ, 1.5๋ฐฐ ๋ฐ 2.0๋ฐฐ๋กœ ๋ณ€ํ™”ํ•˜์˜€๋‹ค. ํšก๋ณด๊ฐ•๊ทผ์˜ ๊ตฌ์†ํšจ๊ณผ๋Š” ๊ธฐ์กด ์—ฐ๊ตฌ์ž๋“ค(Kim et al. 2015; Kim 2016; Yang 2016; Yang and Kim 2016; Yang et al. 2021)์— ๋”ฐ๋ผ ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘ ์‹คํ—˜์œผ๋กœ๋ถ€ํ„ฐ ์–ป์–ด์ง„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์—์„œ, ๊ฐ•๋„์ฆ๊ฐ€๊ณ„์ˆ˜($K_{s}$) ๋ฐ ์ตœ๋Œ€ ์••์ถ•์‘๋ ฅ ์ดํ›„ 85 %์˜ ๋ณ€ํ˜•๋ฅ ($\varepsilon_{c85}$)๋กœ๋ถ€ํ„ฐ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ๋˜ํ•œ ์‹คํ—˜๊ฒฐ๊ณผ๋“ค์„ ๊ธฐ๋ฐ˜์œผ๋กœ 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ ์—ฐ์„ฑ๊ณผ ๋™์ผํ•œ ์„ฑ๋Šฅ์„ ํ™•๋ณดํ•˜๊ธฐ ์œ„ํ•œ LWAC ๊ธฐ๋‘ฅ์˜ $A_{sh}$๋ฅผ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ์ดํ›„์—๋Š” ์‹คํ—˜์˜ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์™€ Razvi and Saatcioglu(1999) ๋ฐ Yang et al.(2021)์˜ ์˜ˆ์ธก๋ชจ๋ธ์„ ๋น„๊ตํ•˜์˜€๋‹ค.

2. ์‹ค ํ—˜

2.1 ์žฌ๋ฃŒ ๋ฐ ๋ฐฐํ•ฉ

๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ตต์€๊ณจ์žฌ ๋ฐ ์ž”๊ณจ์žฌ๋Š” ๋ฐ”ํ…€์• ์‹œ ๋ฐ ์ค€์„คํ†  ๊ธฐ๋ฐ˜์œผ๋กœ ์ œ์กฐ๋œ ์ธ๊ณต๊ฒฝ๋Ÿ‰๊ณจ์žฌ๋ฅผ 100 % ์‚ฌ์šฉํ•˜์˜€๋‹ค. ๋ณดํ†ต์ค‘๋Ÿ‰ ์ฝ˜ํฌ๋ฆฌํŠธ์—์„œ ๊ตต์€๊ณจ์žฌ๋Š” ์•ˆ์‚ฐ์•”์„, ์ž”๊ณจ์žฌ๋Š” ์ฒœ์—ฐ๋ชจ๋ž˜๋ฅผ ์‚ฌ์šฉํ•˜์˜€๋‹ค. Table 1์—๋Š” ์‚ฌ์šฉ๋œ ๊ตต์€๊ณจ์žฌ ๋ฐ ์ž”๊ณจ์žฌ์˜ ๋ฌผ๋ฆฌ์  ํŠน์„ฑ์„ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๊ตต์€๊ณจ์žฌ ๋ฐ ์ž”๊ณจ์žฌ์˜ ์ตœ๋Œ€์น˜์ˆ˜๋Š” ๊ฐ๊ฐ 19 mm ๋ฐ 4.75 mm์ด๋ฉฐ, NWC์—์„œ๋Š” ๊ฐ๊ฐ 19 mm ๋ฐ 4.75 mm์ด๋‹ค. ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ ๋ฐฐํ•ฉ์€ Lee and Yang(2018)์— ์˜ํ•ด ์ˆ˜ํ–‰๋˜์—ˆ๋˜ ์‹ค๋‚ด์‹คํ—˜ ๋ฐฐํ•ฉํ‘œ๋ฅผ ์ด์šฉํ•˜์˜€์œผ๋ฉฐ, ๋ฌผ-์‹œ๋ฉ˜ํŠธ๋น„($W/B$) 55 %๋กœ ์ถฉ๋ถ„ํ•œ ์œ ๋™์„ฑ์„ ํ™•๋ณดํ•˜์—ฌ ๊ณ ์„ฑ๋Šฅ ๊ฐ์ˆ˜์ œ๋ฅผ ์‚ฌ์šฉํ•˜์ง€ ์•Š์•˜๋‹ค. ๋˜ํ•œ LWAC ๋ฐฐํ•ฉ์—์„œ๋Š” ๊ฒฝ๋Ÿ‰๊ณจ์žฌ์˜ ๋†’์€ ํก์ˆ˜์œจ์— ๋”ฐ๋ฅธ ์žฌ๋ฃŒ๋ถ„๋ฆฌ๋ฅผ ๋ฐฉ์ง€ํ•˜๊ธฐ ์œ„ํ•ด์„œ 24์‹œ๊ฐ„ ์‚ฌ์ „์นจ์ˆ˜(pre-wetting)๋ฅผ ์‹ค์‹œ ํ•œ ํ›„ 24์‹œ๊ฐ„ ๋™์•ˆ ๋Œ€๊ธฐ์—์„œ ๊ฑด์กฐ์‹œ์ผœ ํ‘œ๋ฉด๊ฑด์กฐ ์ƒํƒœ๋ฅผ ์œ ์ง€ํ•˜์˜€๋‹ค. ์ฝ˜ํฌ๋ฆฌํŠธ ๋ชฉํ‘œ ์••์ถ•๊ฐ•๋„๋Š” 24 MPa๋กœ ์„ค์ •ํ•˜์˜€๋Š”๋ฐ, ๊ธฐ๋‘ฅ ์‹คํ—˜ ์‹œ ์ธก์ •๋œ LWAC ๋ฐ NWC์˜ ์••์ถ•๊ฐ•๋„๋Š” ๊ฐ๊ฐ 36 MPa ๋ฐ 28 MPa๋กœ ํ‰๊ฐ€๋˜์—ˆ๋‹ค(Table 2).

Table 3์—๋Š” ์‚ฌ์šฉ๋œ ์ฒ ๊ทผ์˜ ์—ญํ•™์  ํŠน์„ฑ์„ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ์ฃผ์ฒ ๊ทผ ๋ฐ ํšก๋ณด๊ฐ•๊ทผ์€ ๊ฐ๊ฐ ์ง๊ฒฝ 16 mm ๋ฐ 13 mm์˜ ์ดํ˜•์ฒ ๊ทผ์„ ์‚ฌ์šฉํ•˜์˜€๋‹ค. ์ฒ ๊ทผ์˜ ํ•ญ๋ณต๊ฐ•๋„ ๋ฐ ํƒ„์„ฑ๊ณ„์ˆ˜๋Š” ์ง๊ฒฝ 16 mm์˜ ๊ฒฝ์šฐ ๊ฐ๊ฐ 457 MPa ๋ฐ 201,501 MPa์ด๋ฉฐ, ์ง๊ฒฝ 13 mm์ธ ๊ฒฝ์šฐ ๊ฐ๊ฐ 457 MPa ๋ฐ 207,336 MPa์ด์—ˆ๋‹ค.

Table 1 Physical properties of the aggregates used

Aggregate type

Maximum size

(mm)

Unit volume weight

(kg/ใŽฅ)

Specific gravity

Water absorption

(%)

Porosity

(%)

$C_{l}$

19

1,400

1.0

19

44.5

$C_{n}$

19

2,600

2.6

20

1.8

$F_{l}$

4.75

1,500

1.1

4.75

37.6

$F_{n}$

4.75

2,580

1.7

4

2.2

Note: $C_{l}$: coarse aggregate of artificially expanded granules; $C_{n}$: coarse aggregate of andesite; $F_{l}$: fine aggregate of artificially expanded granules; $F_{n}$: fine aggregate of andesite
Table 2 Concrete mixture proportions and summary of concrete properties

Concrete type

$S/a$

(%)

$W/B$

(%)

Unit weight (kg/ใŽฅ)

Designed values

Measured values

$W$

$C$

$G$

$S$

$\rho_{cd}$ (kg/ใŽฅ)

$f_{cd}$

(MPa)

$\rho_{c}$

(kg/ใŽฅ)

$f_{ck}$

(MPa)

LWAC

0.47

0.55

195

355

556

503

1,650

24

1,769

36

NWC

0.35

0.50

193

350

1,109

597

2,200

2,280

28

Note: $S/a$: fine aggregate-to-total aggregate ration by volume; $W/B$: water-cement ratio by weight; $W$: water; $C$: ordinary Portland cement; $G$: gravel; $S$: sand; $\rho_{cd}$: designed unit volume weight of concrete; $f_{cd}$: designed compressive strength of concrete; $\rho_{c}$: unit weight of concrete; $f_{ck}$: compressive strength of concrete
Table 3 Mechanical properties of mild deformed bars

Diameter

(mm)

Yield strength

(MPa)

Tensile strength

(MPa)

Elastic modulus

(MPa)

Yield strain

16

457.0

585.5

201,501

0.0024

13

457.0

646.4

207,336

0.0023

2.2 ์‹คํ—˜์ฒด ์ƒ์„ธ

Table 4์™€ Fig. 1์—๋Š” ๊ธฐ๋‘ฅ ์ƒ์„ธ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ํšก๋ณด๊ฐ•๊ทผ ๋ฐฐ๊ทผ๊ฐ„๊ฒฉ($s$)์€ $A_{sh(ACI)}$์˜ 1.0๋ฐฐ, 1.5๋ฐฐ ๋ฐ 2.0๋ฐฐ์— ํ•ด๋‹นํ•˜๋Š” 120 mm, 80 mm ๋ฐ 60 mm์ด๋‹ค. ํ•˜์ง€๋งŒ ํ•˜์ง€๋งŒ Table 4 ๋ฐ Table 5์™€ ๊ฐ™์ด ์‹คํ—˜์ฒด์˜ ์‹ค์ œ ๋‹จ๋ฉด์˜ ํฌ๊ธฐ ๋ฐ ์ธก์ •๋œ $f_{ck}$๋ฅผ ๊ณ ๋ คํ•˜๋ฉด, $A_{sh}$๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ $A_{sh}$๋Š” 0.77, 0.95 ๋ฐ 1.26$A_{sh(ACI)}$๋กœ, NWC ๊ธฐ๋‘ฅ์—์„œ 0.8, 1.5 ๋ฐ 2.0$A_{sh(ACI)}$๋กœ ์‚ฐ์ •๋  ์ˆ˜ ์žˆ๋‹ค. ๋ชจ๋“  ๊ธฐ๋‘ฅ์˜ ์ „์ฒด๋†’์ด๋Š” 1,400 mm์ด๋ฉฐ ์‹คํ—˜๊ตฌ๊ฐ„์˜ ๋†’์ด๋Š” 600 mm์ด๋‹ค. ์ด๋•Œ์˜ ํ˜•์ƒ๋น„($h_{n}/B$)๋Š” ์•ฝ 2.0 ์ธ๋ฐ, ์—ฌ๊ธฐ์„œ $h_{n}$๋Š” ์‹คํ—˜์ฒด์˜ ์ „์ฒด ๋†’์ด๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ๊ธฐ๋‘ฅ ์ƒ๋ถ€ ๋ฐ ํ•˜๋ถ€์—๋Š” ๋น„์‹คํ—˜๊ตฌ๊ฐ„์—์„œ ์ง€์•• ๋ฐ ์••์ถ•ํŒŒ๊ดด๋ฅผ ๋ฐฉ์ง€ํ•˜๊ธฐ ์œ„ํ•˜์—ฌ 500 mmร—500 mmร—400 mm์˜ ์Šคํ„ฐ๋ธŒ๊ฐ€ ์„ค์น˜๋˜์—ˆ๋‹ค. ๊ธฐ๋‘ฅ์˜ ์ฃผ์ฒ ๊ทผ์œผ๋กœ์„œ ์ง๊ฒฝ 16 mm์ธ ์ดํ˜•์ฒ ๊ทผ 8๋ณธ์ด ๋ฐฐ๊ทผ๋˜์—ˆ๋‹ค. ๋ชจ๋“  ๊ธฐ๋‘ฅ์—์„œ ํšก๋ณด๊ฐ•์œผ๋กœ์„œ ๋‚ด๋ถ€ ํฌ๋กœ์Šคํƒ€์ด๋Š” ๋ฐฐ๊ทผ๋˜์ง€ ์•Š์•˜๋‹ค. ์‹คํ—˜์ฒด ๋ช…์—์„œ ์ฒซ ๋ฒˆ์งธ ์•ŒํŒŒ๋ฒณ์€ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ข…๋ฅ˜(L=LWAC, N=NWC)์ด๋ฉฐ, ๋‘ ๋ฒˆ์งธ ์ˆซ์ž๋Š” $A_{sh}$(1.0=1.0$A_{sh(ACI)}$, 1.5=1.5$A_{sh(ACI)}$, 2.0=2.0$A_{sh(ACI)}$)์„ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์˜ˆ๋ฅผ ๋“ค์–ด, L-1.0์€ $A_{sh}$์ด $A_{sh(ACI)}$์˜ 1.0๋ฐฐ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์„ ์˜๋ฏธํ•œ๋‹ค.

Fig. 1 Specimen details (units: mm)
../../Resources/KCI/JKCI.2022.34.6.587/fig1.png
Table 4 Test specimens

Type

Concrete type

Designed values

Actual value

$s_{v}$

(mm)

$\rho_{sh}$

$B =D$

(mm)

$C$

(mm)

$\dfrac{A_{sh}}{A_{sh(ACI)}}$

$B =D$

(mm)

$C$

(mm)

$\dfrac{A_{sh}}{A_{sh(ACI)}}$

L-1.0

LWAC

275

30

1.00

280

20

0.77

120

0.02

L-1.5

1.50

285

15

0.95

80

0.03

L-2.0

2.00

275

15

1.26

60

0.03

N-1.0

NWC

1.00

285

23

0.80

120

0.02

N-1.5

1.50

275

28

1.50

80

0.03

N-2.0

2.00

280

34

2.00

60

0.04

Note : $B$: width of column section; $D$: height of column section; $s_{v}$: spacing of transverse reinforcement; $C_{over}$: concrete cover; $A_{sh}$: total area of transverse reinforcement within spacing $s_{v}$; $A_{sh(ACI)}$: minimum $A_{sh}$ specified in ACI 318-19; $\rho_{sh}$: volumetric ratio of transverse reinforcement
Table 5 Test results and comparisons with the predicted axial load capacity ofACI 318-19 (2019)

Concrete type

Specimens

$\rho_{c}$

(kg/ใŽฅ)

$f_{ck}$

(MPa)

$P_{cr}$

(kN)

$P_{n}$

(kN)

$\varepsilon_{n}$

$\varepsilon_{85}$

$\dfrac{P_{n}}{P_{n(ACI)}}$

$\eta_{cr}$

$\eta_{n}$

LWAC

L-1.0

1,738

31

2,209

3,037

0.0029

0.0044

1.08

0.91

1.25

L-1.5

1,769

38

2,901

3,881

0.0029

0.0048

1.18

0.94

1.26

L-2.0

1,769

38

2,718

3,740

0.0031

0.0049

1.20

0.95

1.30

NWC

N-1.0

2,280

30

2,465

3,045

0.0025

0.0062

1.17

1.01

1.25

N-1.5

2,280

30

2,515

3,185

0.0027

0.0079

1.22

1.11

1.40

N-2.0

2,280

24

2,671

3,142

0.0033

0.0094

1.41

1.42

1.67

Note: $\rho_{c}$: unit volume weight of concrete; $f_{ck}$: compressive strength of concrete; $P_{cr}$: initial cracking load; $P_{n}$: peak load; $\varepsilon_{n}$: the strain at the peak load; $\varepsilon_{85}$: strain corresponding to 85 % of $P_{n}$ at the post-peak branch; $P_{n(ACI)}$: nominal axial strength calculated in accordance with the procedure of ACI 318-19; $\eta_{cr}$(=$P_{cr}/(A_{g}f_{ck})$): normalized inclined $P_{cr}$; $\eta_{n}$(=$P_{n}/(A_{g}f_{ck})$): normalized inclined $P_{n}$; $A_{g}$: cross-sectional area of column

2.3 ์…‹ํŒ…์ƒ์„ธ

์ค‘์‹ฌ ์ถ•ํ•˜์ค‘์€ 7,000 kN ์šฉ๋Ÿ‰์˜ ๋งŒ๋Šฅ์žฌ๋ฃŒ์‹œํ—˜๊ธฐ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋ถ„๋‹น 0.0001์˜ ์ถ•๋ณ€ํ˜•๋ฅ  ์†๋„๋กœ ๊ฐ€๋ ฅ ํ•˜์˜€๋‹ค(Fig. 2). ๊ธฐ๋‘ฅ ์ƒ๋ถ€๋Š” ์ถ•ํ•˜์ค‘ ๊ฐ€๋ ฅ ์‹œ ํŽธ์‹ฌ์„ ์ œ์–ดํ•˜๊ธฐ ์œ„ํ•ด ๊ตฌ์ขŒ๋ฅผ ์„ค์น˜ํ•˜์˜€๋‹ค. ๋˜ํ•œ ์ค‘์‹ฌ์ถ•ํ•˜์ค‘์— ๋”ฐ๋ฅธ ๊ธฐ๋‘ฅ์˜ ๋ณ€์œ„๋ฅผ ์ธก์ •ํ•˜๊ธฐ ์œ„ํ•ด 50 mm ์šฉ๋Ÿ‰์˜ ์ „๊ธฐ์‹ ๋ณ€์œ„๊ธฐ(linear voltage displacement transducer, LVDT)๋ฅผ ๊ธฐ๋‘ฅ 4๋ฉด์— ์„ค์น˜ํ•˜์˜€๋‹ค.

Fig. 2 Test setup
../../Resources/KCI/JKCI.2022.34.6.587/fig2.png

3. ์‹คํ—˜๊ฒฐ๊ณผ ๋ฐ ๋ถ„์„

3.1 ๊ท ์—ด์ง„์ „ ๋ฐ ํŒŒ๊ดด๋ชจ๋“œ

Fig. 3์—๋Š” ๊ธฐ๋‘ฅ์˜ ํŒŒ๊ดด๋ชจ๋“œ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n}$)์— ๋„๋‹ฌ์‹œ์ ๊นŒ์ง€์˜ ๊ท ์—ด์ง„์ „์€ ๋ชจ๋“  ๊ธฐ๋‘ฅ์—์„œ ์œ ์‚ฌํ•˜์˜€๋‹ค. ์ดˆ๊ธฐ๊ท ์—ด์€ ๊ธฐ๋‘ฅ ์ค‘์•™๋ถ€์—์„œ ์ˆ˜์ง๋ฐฉํ–ฅ์œผ๋กœ ๋ฐœ์ƒํ•˜์˜€๋Š”๋ฐ, ์ด๋•Œ $P_{n}$์˜ ์•ฝ 72~85 % ์ˆ˜์ค€์ด์—ˆ๋‹ค. ์ดํ›„ ๊ท ์—ด๋“ค์€ ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ๊ธฐ๋‘ฅ์˜ ์ƒ๋ถ€ ๋ฐ ํ•˜๋ถ€๋กœ ํ™•์žฅ๋˜์—ˆ๋‹ค. ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n}$)์‹œ์ ์—์„œ๋Š” ํ”ผ๋ณต์ด ์ผ๋ถ€ ๋ฐ•๋ฆฌ๋˜์—ˆ์œผ๋ฉฐ, ์ฃผ์ฒ ๊ทผ์˜ ์ขŒ๊ตด๋„ ์‹œ์ž‘๋˜์—ˆ๋‹ค. ์ตœ์ข… ํŒŒ๊ดด์‹œ์ ์—์„œ๋Š” ์ฝ”์–ด ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‹ฌ๊ฐํ•œ ์†์ƒ๊ณผ ์ฃผ์ฒ ๊ทผ์˜ ์ขŒ๊ตด๋กœ ์ธํ•ด ์‹คํ—˜์„ ์ข…๋ฃŒํ•˜์˜€๋‹ค. ์ฃผ์ฒ ๊ทผ์˜ ์ขŒ๊ตด๊ธธ์ด๋Š” 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์—์„œ ๊ฐ€์žฅ ์งง์•˜๋‹ค. ๋ชจ๋“  ๊ธฐ๋‘ฅ์€ ๋‚ด๋ถ€ ํšก๋ณด๊ฐ•๊ทผ์ด ์—†์Œ์—๋„ $A_{sh}$์— ๊ด€๊ณ„์—†์ด ํšก๋ณด๊ฐ•๊ทผ์˜ ํ’€๋ฆผํ˜„์ƒ์ด ์—†์—ˆ๋‹ค. ํ•œํŽธ ์ตœ๋Œ€๋‚ด๋ ฅ ๋„๋‹ฌ ์ดํ›„ ์ฝ”์–ด ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์†์ƒ์€ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ ๋” ํฌ๊ฒŒ ๋‚˜ํƒ€๋‚ฌ๋‹ค. ๊ท ์—ด์˜ ๊ณจ์žฌ ๊ด€ํ†ต ๋ฐ ์ทจ์„ฑ์  ์žฌ๋ฃŒํŒŒ๊ดด ํŠน์„ฑ์œผ๋กœ ์ธํ•ด LWAC ๊ธฐ๋‘ฅ์˜ ์ฝ”์–ด์—์„œ ์†์ƒ์ด ๋” ๊ธ‰๊ฒฉํ•˜๊ณ  ๊นŠ๊ฒŒ ๋‚˜ํƒ€๋‚ฌ๋‹ค(Mun et al. 2021).

Fig. 3 Typical failure characteristics of columns
../../Resources/KCI/JKCI.2022.34.6.587/fig3.png

3.2 ์ค‘์‹ฌ์ถ•ํ•˜์ค‘-์ถ•๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„

Fig. 4์—๋Š” ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๋ณ€ํ˜•๋ฅ ์€ 4๊ฐœ์˜ LVDT(linear variable differential transducers)๋กœ ์ธก์ •๋œ ๋ณ€์œ„์— ์‹คํ—˜๊ตฌ๊ฐ„์˜ ๊ธธ์ด๋กœ ๋‚˜๋ˆ„์–ด ์‚ฐ์ •ํ•˜์˜€๋‹ค. ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์—์„œ ์ƒ์Šน๊ตฌ๊ฐ„์€ ๊ท ์—ด ๋ฐœ์ƒ ์ „๊นŒ์ง€ ์„ ํ˜•๊ฑฐ๋™์„ ๋ณด์˜€๋‹ค. ์ƒ์Šน ๊ธฐ์šธ๊ธฐ๋Š” NWC๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์—์„œ ๋‹ค์†Œ ๋‚ฎ์•˜์œผ๋ฉฐ, 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ ๊ธฐ๋‘ฅ์—์„œ ๊ฐ€์žฅ ๋†’์•˜๋‹ค. ์ดˆ๊ธฐ๊ท ์—ด ๋ฐœ์ƒ ์ดํ›„ ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ๋ณ€ํ˜•๋ฅ ์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ์ถ•ํ•˜์ค‘์ด ์™„๋งŒํ•˜๊ฒŒ ์ฆ๊ฐ€ํ•˜์˜€์œผ๋ฉฐ, $P_{n}$ ์ดํ›„ ์ ์ง„์ ์œผ๋กœ ๊ฐ์†Œํ•˜์˜€๋‹ค. ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n}$) ์ดํ›„ ๊ฐ์†Œ ๊ธฐ์šธ๊ธฐ๋Š” $A_{sh}$๊ฐ€ ๊ฐ์†Œํ• ์ˆ˜๋ก NWC๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์—์„œ ๋” ๊ธ‰๊ฒฉํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ ํ•˜๊ฐ• ๊ธฐ์šธ๊ธฐ๋Š” 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์—์„œ ๊ฐ€์žฅ ์ปธ๋‹ค. ์ด๋Š” NWC ๋ณด๋‹ค๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ $A_{sh}$์ด ์ž‘์„์ˆ˜๋ก ๋” ์ทจ์„ฑํŒŒ๊ดด ๊ฑฐ๋™์„ ์˜๋ฏธํ•œ๋‹ค.

Fig. 4 Axial load-strain curves of column specimens
../../Resources/KCI/JKCI.2022.34.6.587/fig4.png

3.3 ์ดˆ๊ธฐ๊ท ์—ด ํ•˜์ค‘($P_{cr}$) ๋ฐ ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n}$)

๊ธฐ๋‘ฅ์˜ ์ดˆ๊ธฐ๊ท ์—ดํ•˜์ค‘($P_{cr}$)๊ณผ $P_{n}$์€ ๋ฌด์ฐจ์›ํ™”ํ•œ ์ดˆ๊ธฐ๊ท ์—ดํ•˜์ค‘($\eta_{cr}=P_{cr}/(A_{g}f_{ck})$)๊ณผ ๋ฌด์ฐจ์›ํ™”ํ•œ ์ตœ๋Œ€๋‚ด๋ ฅ($\eta_{n}=P_{n}/(A_{g}f_{ck})$)์œผ๋กœ ๋ถ„์„ํ•˜์˜€๋Š”๋ฐ, ์ด๋Š” ๊ธฐ๋‘ฅ์˜ ์ „์ฒด ๋‹จ๋ฉด์ ($A_{g}$)์™€ ์ฝ˜ํฌ๋ฆฌํŠธ ์••์ถ•๊ฐ•๋„($f_{ck}$)์˜ ์˜ํ–ฅ์„ ๋ฌด์‹œํ•˜๊ณ  ์„ค์ •๋œ ๋ณ€์ˆ˜๋งŒ์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•จ์ด๋‹ค. ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ธฐ๋‘ฅ์˜ $\eta_{cr}$๋Š” ํ‰๊ท  0.93์œผ๋กœ์„œ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค 20.9 % ๋‚ฎ์•˜์œผ๋ฉฐ, ์ด ๋‚ฎ์Œ์˜ ์ •๋„๋Š” 1.0$A_{sh(ACI)}$๋ณด๋‹ค 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ ๊ธฐ๋‘ฅ์—์„œ 23.2 % ๋” ๋‚ฎ์•˜๋‹ค. ๋ฌด์ฐจ์›ํ™”ํ•œ ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($\eta_{n}$)์€ $\eta_{cr}$์™€ ๋น„์Šทํ•œ ๊ฒฝํ–ฅ์„ ๋ณด์˜€๋‹ค. ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ธฐ๋‘ฅ์˜ $\eta_{n}$์€ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค 11.8 % ๋‚ฎ์•˜์œผ๋ฉฐ, ๊ทธ ๋‚ฎ์Œ์˜ ์ •๋„๋Š” 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ ๊ธฐ๋‘ฅ๋ณด๋‹ค 2.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ ์‹คํ—˜์ฒด์—์„œ 22.2 % ๋” ํ˜„์ €ํ•˜์˜€๋‹ค(Table 5). ํ•œํŽธ, ACI 318-19(2019)์—์„œ ์ œ์‹œํ•˜๋Š” ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($P_{n(ACI)}$)์€ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์ฝ˜ํฌ๋ฆฌํŠธ์™€ ์ฃผ์ฒ ๊ทผ ํ•˜์ค‘ ์ „๋‹ฌ๋ ฅ์˜ ํ•ฉ์œผ๋กœ ์ œ์‹œํ•˜๊ณ  ์žˆ๋‹ค.

(1)
$P_{n(ACI)}=[0.85f_{ck}(A_{g}-A_{s})+f_{y}A_{s}]$

์—ฌ๊ธฐ์„œ, $A_{s}$ ๋ฐ $f_{y}$๋Š” ๊ฐ๊ฐ ์ฃผ์ฒ ๊ทผ์˜ ์ „์ฒด ๋‹จ๋ฉด์  ๋ฐ ํ•ญ๋ณต๊ฐ•๋„๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ๊ธฐ๋‘ฅ์˜ $P_{n}$๊ณผ ACI 318-19(2019)์˜ ๊ณต์นญ ์ถ•์••์ถ• ๋‚ด๋ ฅ์˜ ๋น„($P_{n}/P_{n(ACI)}$)๋Š” ํ‰๊ท  1.21์œผ๋กœ ๋ชจ๋“  ๊ธฐ๋‘ฅ์˜ $P_{n}$์„ ์•ˆ์ „์ธก์œผ๋กœ ์˜ˆ์ธกํ•˜์˜€๋Š”๋ฐ, ๊ทธ ์•ˆ์ „์ธก์˜ ์ •๋„๋Š” $A_{sh}$์ด ๊ฐ์†Œํ• ์ˆ˜๋ก NWC๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์—์„œ ๋” ๋‚ฎ์•˜๋‹ค. ์ด๋•Œ 2.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์˜ $P_{n}/P_{n(ACI)}$๋Š” 1.20์ด์—ˆ์ง€๋งŒ, 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์—์„œ๋Š” 1.08๋กœ ์•ฝ 10 % ๊ฐ์†Œํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ $P_{n}/P_{n(ACI)}$๋Š” 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์—์„œ 1.08์œผ๋กœ ๊ฐ€์žฅ ๋‚ฎ์•˜๋‹ค.

3.4 ์••์ถ• ์—ฐ์„ฑ๋น„($\mu$)

๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์—ฐ์„ฑ์€ Razvi and Saatcioglu(1992)์— ์˜ํ•ด ์ œ์‹œ๋œ ์••์ถ• ์—ฐ์„ฑ๋น„($\mu =\varepsilon_{85}/0.004$)๋กœ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ์ž๋“ค(Han 2009; Kim 2016; Hwang et al. 2019)์€ $\mu$๋ฅผ $w_{sh}$($=\rho_{sh}f_{yh}/f_{ck}$)์™€์˜ ๊ด€๊ณ„๋กœ๋ถ€ํ„ฐ ๊ตฌ์†ํšจ๊ณผ์— ๋Œ€ํ•œ ์—ฐ์„ฑ์„ ๊ฒ€์ฆํ•˜์˜€๋Š”๋ฐ, ์—ฌ๊ธฐ์„œ $f_{yh}$๋Š” ํšก๋ณด๊ฐ•๊ทผ์˜ ํ•ญ๋ณต๊ฐ•๋„๋ฅผ ์˜๋ฏธํ•œ๋‹ค. Fig. 5์—๋Š” ์‹คํ—˜๊ฒฐ๊ณผ, ๊ธฐ์กด NWC ๊ธฐ๋‘ฅ(Nagashima 1992; Yang and Kim 2016) ๋ฐ LWAC ๊ธฐ๋‘ฅ์˜ $\mu$์™€ $w_{sh}$๊ด€๊ณ„(Basset and Uzumeri 1986; Khaloo et al. 1999; Kan et al. 2010; Wu et al. 2018)๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ์••์ถ•์—ฐ์„ฑ๋น„($\mu$)์™€ $w_{sh}$์˜ ๊ด€๊ณ„์—์„œ 1.0$A_{sh(ACI)}$($w_{sh}$=0.3)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ $\mu$๋Š” $w_{sh}$๊ฐ€ ๋น„์Šทํ•œ ์ˆ˜์ค€์˜ LWAC ๊ธฐ๋‘ฅ๋ณด๋‹ค ์•ฝ 27.9 ๏ผ… ๋‚ฎ์•˜๋‹ค. ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ธฐ๋‘ฅ๋“ค์˜ $\mu$๋Š” $w_{sh}$๊ฐ€ ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ์ฆ๊ฐ€ํ•˜์˜€๋Š”๋ฐ, ๊ทธ ์ฆ๊ฐ€ ๊ธฐ์šธ๊ธฐ๋Š” NWC ๊ธฐ๋‘ฅ๋“ค๋ณด๋‹ค ๋‚ฎ์•˜๋‹ค. ํšก๋ณด๊ฐ•๊ทผ ์ฒด์ ์ง€์ˆ˜($w_{sh}$)์˜ ๊ฐ’์ด 0.2~0.3์ผ ๋•Œ์— LWAC ๊ธฐ๋‘ฅ์˜ $\mu$๋Š” NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค 33.6 % ๋‚ฎ์•˜์ง€๋งŒ, $w_{sh}$์˜ ๊ฐ’์ด 0.5~0.6์ผ ๋•Œ์—๋Š” ๊ทธ ์ฐจ์ด๊ฐ€ 41.9 %๋กœ ๋” ํ˜„์ €ํ•˜๊ฒŒ ๋‚ฎ์•˜๋‹ค. ํŠนํžˆ 1.0$A_{sh(ACI)}$($w_{sh}$=0.3)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ $\mu$๋Š” 1.65~1.7์ธ๋ฐ, ์ด ๊ฐ’๋“ค์€ $w_{sh}$๊ฐ€ 0.58~0.65๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ ๋น„์Šทํ•œ ์ˆ˜์ค€์ด์—ˆ๋‹ค. ์ด๋•Œ LWAC ๊ธฐ๋‘ฅ์˜ $w_{sh}$๋ฅผ $A_{sh}$๋กœ ํ™˜์‚ฐํ•˜๋ฉด, 293.13~328.51 ใŽŸ์œผ๋กœ ์•ฝ 1.2$A_{sh(ACI)}$์™€ ๋น„์Šทํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ 1.0$A_{sh(ACI)}$(=253.4 ใŽŸ)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ๊ณผ ๋™๋“ฑํ•œ ์ˆ˜์ค€์˜ $\mu$๋ฅผ ํ™•๋ณดํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ ์ตœ์†Œ 1.2$A_{sh(ACI)}$ ์ด์ƒ์˜ $A_{sh}$์ด ํ•„์š”ํ•œ ๊ฒƒ์œผ๋กœ ์‚ฌ๋ฃŒ๋œ๋‹ค.

Fig. 5 Effect of transverse reinforcement index on axial ductility
../../Resources/KCI/JKCI.2022.34.6.587/fig5.png

3.5 ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„

Fig. 6์—๋Š” ๊ธฐ๋‘ฅ์˜ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ์ค‘์‹ฌ ์ถ•ํ•˜์ค‘-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์—์„œ ํ”ผ๋ณต ์ฝ˜ํฌ๋ฆฌํŠธ ๋ฐ ์ฃผ์ฒ ๊ทผ์ด ๋ถ€๋‹ดํ•˜๋Š” ํ•˜์ค‘์„ ๋บ€ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ํ•˜์ค‘์„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ๋ฉด์ ์œผ๋กœ ๋‚˜๋ˆ„์–ด ์‚ฐ์ •ํ•˜์˜€๋‹ค(Kim 2016). ์ด๋•Œ ๊ตฌ์†๋˜์ง€ ์•Š์€ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” Yang et al.(2014)์˜ ๋ชจ๋ธ์„ ์ด์šฉํ•˜์˜€์œผ๋ฉฐ, ์ฃผ์ฒ ๊ทผ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ์™„์ „ ํƒ„๏ฝฅ์†Œ์„ฑ์œผ๋กœ ๊ฐ€์ •ํ•˜์˜€๋‹ค. ๋ชจ๋“  ๊ธฐ๋‘ฅ์˜ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ์ƒ์Šน๊ตฌ๊ฐ„์—์„œ $A_{sh(ACI)}$์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ์ดˆ๊ธฐ๊ฐ•์„ฑ์ด ์ฆ๊ฐ€ํ•˜์˜€๋‹ค. ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ตœ๋Œ€ ์‘๋ ฅ($f'_{cc}$)์ดํ›„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ฑฐ๋™์€ NWC๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์—์„œ ๋” ์ทจ์„ฑ์  ๊ฒฝํ–ฅ์„ ๋ณด์˜€๋‹ค. ์ด๋•Œ ํ•˜๊ฐ• ๊ธฐ์šธ๊ธฐ๋Š” $A_{sh(ACI)}$๊ฐ€ ๊ฐ์†Œํ• ์ˆ˜๋ก ๋” ์ฆ๊ฐ€ํ•˜์˜€๋‹ค.

Fig. 6 Stress-strain curves of confined concrete calculated from the axial load-strain curves of columns
../../Resources/KCI/JKCI.2022.34.6.587/fig6.png

Fig. 7์—๋Š” X์ถ•๊ณผ Y์ถ•์„ ๊ฐ๊ฐ $f'_{cc}$ ๋ฐ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์ตœ๋Œ€์‘๋ ฅ ์‹œ ๋ณ€ํ˜•๋ฅ ($\varepsilon'_{cc}$)๋กœ ๋ฌด์ฐจ์›ํ™” ์‹œ์ผœ 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๋ฐ 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๊ตฌ์†๋œ LWAC์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” $A_{sh(ACI)}$์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ ๋” ์™„๋งŒํ•œ ๊ธฐ์šธ๊ธฐ๋ฅผ ๋ณด์˜€๋‹ค. 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ ๊ธฐ์šธ๊ธฐ๋Š” ์ƒํ˜ธ ๋น„์Šทํ•˜์˜€๋‹ค. 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์˜ $w_{sh}$๋Š” 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค ์•ฝ 1.6๋ฐฐ ์ปธ๋‹ค. ์ด๋ฅผ $A_{sh(ACI)}$๋กœ ํ™˜์‚ฐํ•˜๋ฉด NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์—์„œ $A_{sh}$๊ฐ€ ์•ฝ 1.2๋ฐฐ ์ด์ƒ์œผ๋กœ ํ™•์ธํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์—์„œ ์–ป์–ด์ง„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ ๊ณผ ๋™๋“ฑํ•œ ์ˆ˜์ค€์˜ ์—ฐ์„ฑ์„ ํ™•๋ณดํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ ์ตœ์†Œ 1.2$A_{sh(ACI)}$์ด์ƒ์˜ $A_{sh}$์ด ํ•„์š”ํ•  ์ˆ˜ ์žˆ๋‹ค๊ณ  ์‚ฌ๋ฃŒ๋œ๋‹ค.

Fig. 7 Typical normalized stress-strain curves of confined concrete obtained in columns
../../Resources/KCI/JKCI.2022.34.6.587/fig7.png

3.6 ํšก๋ณด๊ฐ•๊ทผ์˜ ์ฝ˜ํฌ๋ฆฌํŠธ ๊ตฌ์†ํšจ๊ณผ ํ‰๊ฐ€

Table 6์—๋Š” LWAC ๋ฐ NWC ๊ธฐ๋‘ฅ์˜ $K_{s}$ ๋ฐ $\varepsilon_{c85}$์„ ์š”์•ฝํ•˜์—ฌ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. Fig. 8์—๋Š” ์‹คํ—˜๊ฒฐ๊ณผ์™€ ๊ธฐ์กด NWC ๊ธฐ๋‘ฅ(Nagashima 1992; Yang and Kim 2016) ๋ฐ LWAC ๊ธฐ๋‘ฅ(Basset and Uzumeri 1986; Khaloo et al. 1999; Kan et al. 2010; Wu et al. 2018)์˜ $K_{s}$ ๋ฐ $\varepsilon_{c85}$๋ฅผ $w_{sh}$์™€์˜ ๊ด€๊ณ„๋กœ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค.

(2)
$K_{s}= f'_{cc}/(0.85f_{ck})$

Fig. 8์—๋Š” ์‹คํ—˜๊ฒฐ๊ณผ, ๊ธฐ์กด NWC ๊ธฐ๋‘ฅ(Nagashima 1992; Yang and Kim 2016) ๋ฐ ๊ธฐ์กด LWAC ๊ธฐ๋‘ฅ์˜ ์‹คํ—˜๊ฒฐ๊ณผ(Basset and Uzumeri 1986; Khaloo et al. 1999; Kan et al. 2010; Wu et al. 2018)์— ๋”ฐ๋ฅธ $K_{s}$ ๋ฐ $\varepsilon_{c85}$๋ฅผ $w_{sh}$์™€์˜ ๊ด€๊ณ„๋กœ ๋‚˜ํƒ€๋‚ด์—ˆ๋‹ค. ๊ฐ•๋„์ฆ๊ฐ€๊ณ„์ˆ˜($K_{s}$)์™€ $w_{sh}$์˜ ๊ด€๊ณ„์—์„œ 1.0$A_{sh(ACI)}$($w_{sh}$=0.3)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ $K_{s}$ ๋ฐ $\varepsilon_{c85}$๋Š” $w_{sh}$๊ฐ€ ๋น„์Šทํ•œ ์ˆ˜์ค€์˜ LWAC ๊ธฐ๋‘ฅ๋ณด๋‹ค ๊ฐ๊ฐ ํ‰๊ท  40.9 ๏ผ… ๋ฐ 43.3 ๏ผ… ๋‚ฎ์•˜๋‹ค. ๊ธฐ๋‘ฅ์˜ $K_{s}$ ๋ฐ $\varepsilon_{c85}$๋Š” $w_{sh}$์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ํ–ฅ์ƒ๋˜์—ˆ์œผ๋ฉฐ, ๊ทธ ์ฆ๊ฐ€ ๊ธฐ์šธ๊ธฐ๋Š” NWC๋ณด๋‹ค LWAC ๊ธฐ๋‘ฅ์ด ๋” ๋‚ฎ์•˜๋‹ค. ํšก๋ณด๊ฐ•๊ทผ ์ฒด์ ์ง€์ˆ˜($w_{sh}$)์˜ ๊ฐ’์ด 0.2~0.3์ผ ๋•Œ LWAC ๊ธฐ๋‘ฅ์˜ $K_{s}$๋Š” NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค ๊ฐ๊ฐ 25.8 % ๋‚ฎ์•˜์œผ๋ฉฐ, $w_{sh}$์˜ ๊ฐ’์ด 0.5~0.6์ผ ๋•Œ์—๋Š” 26.3 % ๋‚ฎ์€ ์ˆ˜์ค€์œผ๋กœ ๊ทธ ์ฐจ์ด๋Š” ๋ฏธ๋ฏธํ•˜์˜€๋‹ค. ๋งˆ์ฐฌ๊ฐ€์ง€๋กœ LWAC ๊ธฐ๋‘ฅ์˜ $\varepsilon_{c85}$๋Š” $w_{sh}$์˜ ๊ฐ’์ด 0.2~0.3์ผ ๋•Œ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค ๊ฐ๊ฐ 60.8 %, $w_{sh}$์˜ ๊ฐ’์ด 0.5~0.6์ผ ๋•Œ 53.9 % ๋‚ฎ์€ ์ˆ˜์ค€์ด์—ˆ๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ $K_{s}$๋Š” 1.0$A_{sh(ACI)}$($w_{sh}$=0.3)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์—์„œ 1.64~1.90์ธ๋ฐ, ์ด ๊ฐ’๋“ค์€ $w_{sh}$๊ฐ€ 0.65~0.75๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ ๋น„์Šทํ•œ ์ˆ˜์ค€์ด์—ˆ๋‹ค. ์ด๋•Œ 0.65~0.75 ๋ฒ”์œ„์˜ $w_{sh}$๋ฅผ $A_{sh}$๋กœ ํ™˜์‚ฐํ•˜๋ฉด, 328.51~379.05 ใŽŸ์ด๋‹ค. ์ด์— ๋”ฐ๋ผ 1.0$A_{sh(ACI)}$ (=253.4 ใŽŸ)๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ๊ณผ ๋™๋“ฑํ•œ ์ˆ˜์ค€์˜ $K_{s}$๋ฅผ ํ™•๋ณดํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” ๊ฐ๊ฐ ์ตœ์†Œ 1.3$A_{sh(ACI)}$์ด์ƒ์ด ํ•„์š”ํ•œ ๊ฒƒ์œผ๋กœ ์‚ฌ๋ฃŒ๋œ๋‹ค. ํ•œํŽธ, Fig. 8์€ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๊ฐ€ ์ œ์‹œ๋œ ๋…ผ๋ฌธ์˜ ์‹คํ—˜๊ฒฐ๊ณผ(Khaloo et al. 1999; Nagashima 1992; Yang and Kim 2016)๋งŒ์„ ์ด์šฉํ•˜์—ฌ ๋น„๊ตํ•˜์˜€๋‹ค.

Fig. 8 Effect of transverse reinforcement index on confinement effect
../../Resources/KCI/JKCI.2022.34.6.587/fig8.png
Table 6 Summary of values for confined concrete

Specimens

$w_{sh}$

$f_{cc}$

(MPa)

$K_{s}$

$\varepsilon_{c85}$

L1.0

0.29

32.4

1.23

0.0048

L1.5

0.36

43.6

1.35

0.0058

L2.0

0.48

48.2

1.49

0.0060

N1.0

0.3

34.4

1.35

0.0074

N1.5

0.46

39.5

1.55

0.0101

N2.0

0.76

40.4

1.99

0.0117

Note: $w_{sh}$: transverse reinforcement index calculated using the actual section dimension and material strengths; $f_{cc}$: compressive strength of confined concrete; $K_{s}$: strength gain factor of confined concrete; $\varepsilon_{85}$: strain corresponding to 85 % of the peak stress beyond strain at the peak stress

3.7 ๊ธฐ์กด ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์™€ ์‹คํ—˜๊ฒฐ๊ณผ์˜ ๋น„๊ต

Fig. 9์—๋Š” ์ถ•ํ•˜์ค‘-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋กœ๋ถ€ํ„ฐ ์–ป์–ด์ง„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ Razvi and Saatcioglu(1999) ๋ฐ Yang et al.(2021)์˜ ์˜ˆ์ธก๋ชจ๋ธ๊ณผ ๋น„๊ตํ•˜์˜€๋‹ค. ์ œ์•ˆ๋ชจ๋ธ๊ณผ ์‹คํ—˜๊ฒฐ๊ณผ์˜ ๋น„๊ต๋Š” NRMSE(normalized root mean square error)๊ฐ’์„ ์ตœ๋Œ€์‘๋ ฅ ์ด์ „ ๋ฐ ์ดํ›„์˜ ์ƒ์Šน๊ตฌ๊ฐ„๊ณผ ํ•˜๊ฐ•๊ตฌ๊ฐ„์œผ๋กœ ๊ตฌ๋ถ„ํ•˜์—ฌ ์‚ฐ์ •ํ•˜์˜€๋‹ค(Table 7). Razvi and Saatcioglu(1999)์˜ ๋ชจ๋ธ์€ ์ƒ์Šน๊ตฌ๊ฐ„์—์„œ NWC ๊ธฐ๋‘ฅ๊ณผ ์œ ์‚ฌํ•˜์˜€๋‹ค. ์‹คํ—˜๊ฒฐ๊ณผ๊ฐ’ ๋Œ€๋น„ ์˜ˆ์ธก๊ฐ’์— ๋Œ€ํ•œ NRMSE์˜ ํ‰๊ท ($\gamma_{m}$)์€ LWAC ๊ธฐ๋‘ฅ์—์„œ 0.188์œผ๋กœ 0.100์ธ NWC ๊ธฐ๋‘ฅ๋ณด๋‹ค ๋‚ฎ์•˜๋‹ค. ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ๋„ ์‹คํ—˜๊ฒฐ๊ณผ๊ฐ’ ๋Œ€๋น„ ์˜ˆ์ธก๊ฐ’์— ๋Œ€ํ•œ NRMSE์˜ $\gamma_{m}$๋Š” LWAC ๊ธฐ๋‘ฅ์—์„œ 0.583์œผ๋กœ 0.088์ธ LWAC ๊ธฐ๋‘ฅ๋ณด๋‹ค ์ผ์น˜์„ฑ์ด ๋‚ฎ์•˜๋‹ค. ์ด๋Š” Razvi and Saatcioglu(1999)์˜ ๋ชจ๋ธ์ด ์ƒ์Šน ๋ฐ ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ ๊ตฌ์†๋œ LWAC์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ ๋‹ค์†Œ ๊ณผ๋Œ€ํ‰๊ฐ€ ํ•œ๋‹ค๋Š” ๊ฒƒ์„ ์˜๋ฏธํ•œ๋‹ค. ๋ฐ˜๋ฉด, Yang et al.(2021)์˜ ๋ชจ๋ธ์€ ๋ชจ๋“  ๊ธฐ๋‘ฅ์˜ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋ฅผ ์ž˜ ์˜ˆ์ธกํ•˜์˜€๋‹ค. ์ด๋•Œ LWAC ๊ธฐ๋‘ฅ์˜ ์ƒ์Šน๊ตฌ๊ฐ„ ๋ฐ ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ ๊ฐ๊ฐ 0.059 ๋ฐ 0.087์ด์—ˆ์œผ๋ฉฐ, NWC ๊ธฐ๋‘ฅ์—์„œ๋Š” ๊ฐ๊ฐ 0.052 ๋ฐ 0.041์ด์—ˆ๋‹ค. ์ด ๊ฐ’๋“ค์€ Razvi and Saatcioglu(1999)์˜ ๋ชจ๋ธ์—์„œ ์–ป์–ด์ง„ ๊ฐ’๋ณด๋‹ค ํ˜„์ €ํžˆ ๋‚ฎ์•˜๋‹ค. ๋”ฐ๋ผ์„œ Yang et al.(2021)์˜ ๋ชจ๋ธ์€ NWC ๋Œ€๋น„ LWAC์—์„œ ๊ฐ์†Œํ•˜๋Š” ๊ตฌ์†ํšจ๊ณผ์˜ ํ•ฉ๋ฆฌ์ ์œผ๋กœ ํ‰๊ฐ€ํ•  ์ˆ˜ ์žˆ์œผ๋ฏ€๋กœ, ์ถ•๋ ฅ๋ถ€์žฌ์˜ ๋‚ด๋ ฅ ๋ฐ ์—ฐ์„ฑ์„ ํšจ์œจ์ ์œผ๋กœ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋‹ค.

Fig. 9 Comparisons of experimental stress-strain curves of confined concrete and the prediction model(Razvi and Saatcioglu 1999;Yang et al. 2021)
../../Resources/KCI/JKCI.2022.34.6.587/fig9.png
Table 7 Comparison of NRMSE obtained from experimental stress-strain curve

Concrete type

Specimens

NRMSD (normalized root mean square error)

Ascending branch

Descending branch

Razvi and Saatcioglu

(1999)

Yang et al.

(2021)

Razvi and Saatcioglu

(1999)

Yang et al.

(2021)

LWAC

L-1.0

0.210

0.063

0.876

0.115

L-1.5

0.222

0.063

0.500

0.064

L-2.0

0.134

0.053

0.372

0.082

$\gamma_{m}$

0.188

0.059

0.583

0.087

NWC

N-1.0

0.113

0.055

0.081

0.035

N-1.5

0.089

0.051

0.065

0.044

N-2.0

0.098

0.049

0.119

0.043

$\gamma_{m}$

0.100

0.052

0.088

0.041

4. ๊ฒฐ ๋ก 

์ด ์—ฐ๊ตฌ์—์„œ๋Š” ํšก๋ณด๊ฐ•๊ทผ ์–‘($A_{sh}$)์ด ๊ฒฝ๋Ÿ‰๊ณจ์žฌ ์ฝ˜ํฌ๋ฆฌํŠธ(lightweight aggregate concrete, LWAC) ๊ธฐ๋‘ฅ์˜ ์••์ถ•๊ฑฐ๋™์— ๋ฏธ์น˜๋Š” ์˜ํ–ฅ์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ๋™์ผ ์„ค๊ณ„์กฐ๊ฑด์˜ ๋ณดํ†ต์ค‘๋Ÿ‰ ์ฝ˜ํฌ๋ฆฌํŠธ(normal-weight concrete, NWC) ๊ธฐ๋‘ฅ์˜ ์••์ถ•์—ฐ์„ฑ ๋ฐ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๋น„๊ต๋กœ๋ถ€ํ„ฐ LWAC ๊ธฐ๋‘ฅ์—์„œ $A_{sh}$์˜ ์ตœ์†Ÿ๊ฐ’์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ๊ทธ ๊ฒฐ๊ณผ ๋‹ค์Œ๊ณผ ๊ฐ™์€ ๊ฒฐ๋ก ์„ ์–ป์—ˆ๋‹ค.

1) ๋ฌด์ฐจ์›ํ™”ํ•œ ์ตœ๋Œ€ ์••์ถ•๋‚ด๋ ฅ($\eta_{n}$)์€ NWC๋ณด๋‹ค LWAC์—์„œ ํ‰๊ท  11.8 % ๋‚ฎ์•˜๋Š”๋ฐ, ๊ทธ ๋‚ฎ์Œ์˜ ์ •๋„๋Š” ACI 318-19์—์„œ ์ œ์‹œํ•˜๋Š” ์ตœ์†Œ ํšก๋ณด๊ฐ•๊ทผ ์–‘($A_{sh(ACI)}$)์ด ์ฆ๊ฐ€ํ•จ์— ๋”ฐ๋ผ ๋” ํ˜„์ €ํ•˜์˜€๋‹ค. ๊ฒฐ๊ณผ์ ์œผ๋กœ ACI 318-19์˜ ๊ณต์นญ๋‚ด๋ ฅ์˜ ๋น„($P_{n}/P_{n(ACI)}$)๋Š” 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์—์„œ 1.08์œผ๋กœ ๊ฐ€์žฅ ๋‚ฎ์•˜๋‹ค.

2) ์••์ถ•์—ฐ์„ฑ๋น„($\mu$)๋Š” 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์—์„œ 1.65~1.7์ด์—ˆ๋Š”๋ฐ, ์ด๋“ค ๊ฐ’๋“ค์€ 1.2$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ ๋น„์Šทํ•œ ์ˆ˜์ค€์ด์—ˆ๋‹ค.

3) ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„๋Š” ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์—์„œ ์ƒํ˜ธ ์œ ์‚ฌํ•˜์˜€๋‹ค. ์ด๋•Œ 2.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ์˜ ํšก๋ณด๊ฐ•๊ทผ ์ฒด์ ์ง€์ˆ˜($w_{sh}$)๋Š” 1.0$A_{sh(ACI)}$์œผ๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์˜ $w_{sh}$๋ณด๋‹ค 1.6๋ฐฐ ๋” ์ปธ๋‹ค.

4) ๊ฐ•๋„์ฆ๊ฐ€๊ณ„์ˆ˜($K_{s}$)๋Š” 1.0$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ NWC ๊ธฐ๋‘ฅ์—์„œ 1.64~1.90์ž„์„ ๋ณด์˜€๋‹ค. ์ด ๊ฐ’๋“ค์€ 1.3$A_{sh(ACI)}$๋กœ ๋ฐฐ๊ทผ๋œ LWAC ๊ธฐ๋‘ฅ๊ณผ ๋น„์Šทํ•œ ์ˆ˜์ค€์ด์—ˆ๋‹ค.

5) Razvi and Saatcioglu(1999)์˜ ๋ชจ๋ธ์€ LWAC ๊ธฐ๋‘ฅ์—์„œ ์–ป์–ด์ง„ ๊ตฌ์†๋œ ์ฝ˜ํฌ๋ฆฌํŠธ์˜ ์‘๋ ฅ-๋ณ€ํ˜•๋ฅ  ๊ด€๊ณ„์˜ ์ƒ์Šน๊ตฌ๊ฐ„๋ณด๋‹ค ํ•˜๊ฐ•๊ตฌ๊ฐ„์—์„œ ๊ทธ ์ผ์น˜์„ฑ์ด ํ˜„์ €ํ•˜๊ฒŒ ๋‚ฎ์•˜๋‹ค. ๋ฐ˜๋ฉด, ํšก๋ณด๊ฐ•๊ทผ์˜ ๊ตฌ์†๋ ฅ์— ๋Œ€ํ•œ ๊ธฐํ•˜ํ•™์  ํฌ๊ธฐ ๋ฐ ์ฝ˜ํฌ๋ฆฌํŠธ ์ทจ์„ฑ๋„์˜ ์˜ํ–ฅ์„ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋Š” Yang et al.(2021)์˜ ๋ชจ๋ธ์€ ์‹คํ—˜๊ฒฐ๊ณผ๋ฅผ ์ž˜ ์˜ˆ์ธกํ•˜์˜€๋‹ค.

6) NWC ๊ธฐ๋‘ฅ๊ณผ ๋™๋“ฑ ์ˆ˜์ค€์—์„œ LWAC ๊ธฐ๋‘ฅ์˜ ์••์ถ•๊ฑฐ๋™์„ ๊ณ ๋ คํ•˜๋ฉด ACI 318-19์—์„œ ์š”๊ตฌํ•˜๋Š” ์ตœ์†Œ $A_{sh}$์€ LWAC ๊ธฐ๋‘ฅ์—์„œ ์•ฝ 1.2~1.3๋ฐฐ ์ฆ๊ฐ€์‹œํ‚ฌ ํ•„์š”๊ฐ€ ์žˆ๋‹ค.

๊ฐ์‚ฌ์˜ ๊ธ€

์ด ๋…ผ๋ฌธ์€ ์ •๋ถ€(๊ต์œก๋ถ€)์˜ ์žฌ์›์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ์˜ ์ง€์›์„ ๋ฐ›์•„ ์ˆ˜ํ–‰๋œ ๊ธฐ์ดˆ์—ฐ๊ตฌ์‚ฌ์—…(No. 2018R1D1A1B0705027515) ๋ฐ 2022๋…„๋„ ์ •๋ถ€(๊ณผํ•™๊ธฐ์ˆ ์ •๋ณดํ†ต์‹ ๋ถ€)์˜ ์žฌ์›์œผ๋กœ ํ•œ๊ตญ์—ฐ๊ตฌ์žฌ๋‹จ์˜ ์ง€์›์„ ๋ฐ›์•„ ์ˆ˜ํ–‰๋œ ์—ฐ๊ตฌ(No. 2022R1A2B5B03002 476)์ด๋ฉฐ, 2022ํ•™๋…„๋„ ๊ฒฝ๊ธฐ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› ์—ฐ๊ตฌ์›์žฅํ•™์ƒ ์žฅํ•™๊ธˆ ์ง€์›์— ์˜ํ•˜์—ฌ ์ˆ˜ํ–‰๋œ ์—ฐ๊ตฌ์ž„.

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