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1 Journal of the Korea Concrete Institute Vol. 27, No. 3, pp. 252~262, June, pissn eissn 초고강도강섬유보강콘크리트의인장강도와압축강도사이의상관관계에관한연구 배백일 1) 최현기 2) * 최창식 3) 1) 한양대학교산업과학연구소 2) 경남대학교소방방재공학과 3) 한양대학교건축공학부 Correlation Between Tensile Strength and Compressive Strength of Ultra High Strength Concrete Reinforced with Steel Fiber Baek-Il Bae, 1) Hyun-Ki Choi, 2) * and Chang-Sik Choi 3) 1) Research Institute of Industrial, Hanyang University, Seoul, , Korea 2) Dept of Fire and Disaster Prevention Engineering, KyungNam University, ChangWon, , Korea 3) Dept of Architectural Engineering, Hanyang University, Seoul, , Korea ABSTRACT Ultra-high strength concrete which have 100 MPa compressive strength or higher can be developed applying RPC(Reactive Powder Concrete). Preventing brittle failure under compression and tension, ultra-high strength concrete usually use the steel fibers as reinforcements. For the effective use of steel fiber reinforced ultra-high strength concrete, estimation of tensile strength is very important. However, there are insufficient research results are available with no relation between them. Therefore, in this study, correlation between compressive strength and tensile strength of ultra-high strength concrete was investigated by test and statistical analysis. According to test results, increasing tendency of tensile strength was also shown in the range of ultra-high strength. Evaluation of test results of this study and collected test results were carried out. Using 284 splitting test specimens and 265 flexural test specimens, equations suggested by previous researchers cannot be applied to ultra-high strength concrete. Therefore, using database and test results, regression analysis was carried out and we suggested new equation for splitting and flexural tensile strength of steel fiber reinforced ultra-high strength concrete. Keywords : steel fiber reinforced ultra-high strength concrete, splitting strength, flexural strength, regression analysis 1. 서론 1) 콘크리트는낮은인장강도에의해인장응력하에서쉽게균열이발생하는재료로알려져있다. 이는콘크리트가보유한낮은인장강도에의한것으로철근콘크리트구조의성립이후해당문제를해결하기위한많은노력이이어져왔다. 최근콘크리트의낮은인장강도에의해발생하는문제를해결하기위해콘크리트의인장강도를증진시키고자하는노력이진행되고있으며, 이는매트릭스의고강도화와강섬유의혼입을통해이루어지고있다. 현행설계기준 1) 에의해철근콘크리트구조물을설계할때콘크리트의압축강도가주요설계인자가된다. c 라성능기반설계가사용되면서콘크리트의압축강도뿐만아니라다른기계적특성을필요로하는경우가많아지고있는추세이다. 특히섬유가혼입된고강도콘크리트를사용할때에는이러한성질들에대한평가가필수적으로수반되어야한다. 일반적으로성능기반설계에사용되는섬유로보강된고강도콘크리트의기계적성질로는인장강도와응력-변형률관계이다. 콘크리트의인장강도는일반적으로직접인장시험, 쪼갬인장강도시험 2) 그리고휨인장강도시험 3) 을통해결정한다. 그러나직접인장강도시험은시험방법의다양성과시험장치의특수성때문에시험결과의분산이큰편이다. 이에따라철근콘크리트구조물의설계에는표준기관에서정해놓은쪼갬인장강도와휨인장강도시험법에의거한값을사용한다. 또한구조설계기준과섬유보강콘크리트와고강도콘크리트의기수행된연구결과 4) 에따르면쪼갬인장강도와휨인장강도는콘크리트의압축강도제곱근또는세제곱근에회기분석등에의해결정된계수를 252

2 곱하여결정하는것을제안하고있다. 그러나해당연구결과들은사용가능한명확한강도의제한이있으므로최근성능기반설계기법을사용하여설계되는초고강도콘크리트기계적특성의정의에는사용하기어렵다. 따라서본연구에서는섬유로보강된고강도콘크리트의설계에적용하기위해현재사용되고있는실험식들의한계를벗어나는범주에서도사용가능한기계적특성중인장강도의추정식을도출하고자한다. 확인할수있으며이지수들은 0~1 사이의값을가지는것을확인할수있다. 일반적으로많이사용되는값은 1/2이나 2/3인것으로나타나고있으나, 연구결과가고강도콘크리트를반영해갈수록지수가증가하는것을확인할수있다. 특히, ACI318-11에서정의하고있는파괴계수는 KCI에서제안하고있는계수와같은개념으로도출되었으며유사한값이므로국내설계기준의값을대변하는것으로판단하였다. 2. 섬유보강고강도콘크리트의인장강도 2.2 섬유보강콘크리트의인장강도 섬유보강콘크리트와고강도콘크리트의압축강도에기반한인장강도의추정에대한기존연구결과를분석하면다음과같다. 2.1 고강도콘크리트의인장강도 고강도콘크리트의쪼갬인장강도와휨인장강도에대한추정식은여러연구자들에의해제안되었으며 Table 1과 2에각각정리하여나타내었다. 콘크리트의인장강도로대변되는두지표는모두콘크리트압축강도에대한지수함수형태로결정되는것을 Table 1 Splitting strength estimation Researcher Equation Limitation Carrasquillo 5) Mokhtarzadeh 6) Nihal Arιoglu 7) M.F.M. Zain 8) Oluokun 9) Ahmad 10) ACI ) NZS ) : splitting strength of concrete(mpa) : characteristic compressive strength of concrete(mpa) Table 2 Flexural strength estimation Researcher Equation Limitation Carrasquillo 5) Burg 13) Khayat 14) Ahmad 10) ACI ) NZS ) : modulus of rupture(mpa) : compressive strength of concrete(mpa) 섬유보강콘크리트의쪼갬인장강도와휨인장강도에대한추정식또한여러연구자들에의해제안되었으며 Table 3 와 4에각각정리하여나타내었다. 섬유로보강되어있지않은콘크리트와달리섬유로보강된콘크리트의인장강도추정을위한제안식들은두가지형태로분류되는것을확인할수있다. 강섬유로보강되어있지않은, 일반적인콘크리트와같이콘크리트의압축강도만으로정의하는경우가있으며, 강섬유의영 Table 3 Splitting strength estimation Researcher Equation Limitation Narayannan 1 5) - Wafa 16) Song 17) Thomas 18) Ramadoss 19) - : splitting strength of fiber reinforced concrete (MPa), : cube strength of fiber concrete (MPa), : fiber factor, : length of the fiber (mm), : diameter of the fiber (mm), : volume fraction of fibers, : bond factor Table 4 Flexural strength estimation Researcher Equation Limitation Wafa 16) Song 17) (150x150x530 prism) (100x100x350 prism) Thomas 18) Ramadoss 19) - : modulus of rupture of fiber reinforced concrete (MPa), : cube strength of fiber concrete (MPa), : characteristic compressive strength of concrete (MPa), : Reinforcing Index ( ), : length of the fiber (mm), : diameter of the fiber (mm), : volume fraction of fibers, : bond factor 초고강도강섬유보강콘크리트의인장강도와압축강도사이의상관관계에관한연구 253

향을반영하기위한새로운변수를적용하는경우도있다. 이경우콘크리트의인장강도를결정하는요인은섬유의응력전달능력이므로섬유의형태와혼입량을반영하기위해보강지수 (RI : Reinforcing Index) 를사용하여보강된섬유의양에의거하여인장강도를결정하는것을확인할수있었다. 여기서보강지수는섬유의혼입량과섬유의형상비를반영한지수로다음식 (1) 과같이정의할수있다.

기존에수행된연구에따르면보강지수에대한 1차또는 2차식의형태를가지며특수한경우지수함수의형태로섬유의영향을반영하게된다. 그러나섬유의영향을반영하는추정식의모든경우매트릭스의인장강도에대한섬유영향의대수합으로이루어지는것을확인할수있었다. (a) Compressive Strength Test (b) Splitting Strength Test 3.

3 향을반영하기위한새로운변수를적용하는경우도있다. 이경우콘크리트의인장강도를결정하는요인은섬유의응력전달능력이므로섬유의형태와혼입량을반영하기위해보강지수 (RI : Reinforcing Index) 를사용하여보강된섬유의양에의거하여인장강도를결정하는것을확인할수있었다. 여기서보강지수는섬유의혼입량과섬유의형상비를반영한지수로다음식 (1) 과같이정의할수있다. (1) 여기서 는섬유의혼입량, 은섬유의길이, 는섬유의지름을의미하며, 해당보강지수는무차원화되어있는값이다. 섬유의보강량을반영한인장강도의결정식또한, 일반적인콘크리트의인장강도를결정하기위한식과같이회기분석을통해결정되므로, 여러연구자들에의해다양한형태의추정식이제안되었다. 기존에수행된연구에따르면보강지수에대한 1차또는 2차식의형태를가지며특수한경우지수함수의형태로섬유의영향을반영하게된다. 그러나섬유의영향을반영하는추정식의모든경우매트릭스의인장강도에대한섬유영향의대수합으로이루어지는것을확인할수있었다. (a) Compressive Strength Test (b) Splitting Strength Test 3. 초고강도강섬유보강콘크리트의기계적성질 고강도콘크리트와섬유보강콘크리트의기계적성질에대한기존연구들의검토결과명확한강도제한이존재하고있으며해당제한치를벗어날경우큰폭의편차가나타나게될것으로예상된다. 따라서본연구에서는현재설계기준또는연구결과에서정하고있는강도제한을벗어났을경우기존콘크리트인장강도추정식의적합성을평가하고, 100 MPa 이상에서의초고강도콘크리트의특성을반영한추정식을도출하기위해 80~200 MPa 사이의압축강도를보유한콘크리트의압축및간접적인장강도시험을수행하였다. Fig. 1 Test Setup (c) Flexural Strength Test Table 5 Material properties of steel fiber Type Yield strength (MPa) Elastic Modulus (GPa) Length (mm) Diameter (mm) Straight 실험계획기존연구결과에대한검토로부터도출된결과에따라본연구에서는매트릭스의압축강도와섬유의혼입량을주요변수로설정하였다. 압축강도의범위는 80, 100, 150, 200 MPa로설정하였으며, 최근초고강도콘크리트의제작에빈번하게적용되며상용화에이르고있는 RPC의개념을적용하여제작하였다. 섬유의혼입량은기존연구결과 20) 로나타난사용처별로일반적으로구분되는섬유의혼입량에근거하여 0.5%, 1.0%, 2% 의부피비로혼입하는것으로결정하였다. 각각의배합별로 φ100x200 (mm) 원주형공시체를압축시험용으로세개제작하였으며, 쪼갬인장강도시험을위해세개를추가제작하였 다. 또한휨인장강도시험을위해 500x100x100 (mm) 직육면체시험체를세개제작하였다. 각시험체의시험은각각 KS F ), KS F 2423 그리고 KS F 2408에의해수행되었다. 각시험체의설치상황과함께일반적인파괴상황을 Fig. 1에나타내었다. 사용된강섬유의제원을 Table 5에정리하여나타내었으며, 사용된콘크리트의배합비를매트릭스가보유한압축강도에따라 Table 6에정리하여나타내었다. Table 6에나타난바와같이초고강도의발현을위해매트릭스의물-결합재비가보통콘크리트에비해매우낮은상태이다. 이와함께강섬유의혼입에의해발생할수있는시공연도의상실을방지하기위해배합비에나타난바와같은초고성능감수제를사용하였다. 254 한국콘크리트학회논문집제 27 권제 3 호 (2015)

4 Table 6 Mix proportion ID w/b Weight (kg/m 3 ) Cement Water Silica Fume Sand Filler Steel Fiber Super-Plasticizer f ,74, f ,74, f ,74, f ,74, Table 7 Test Results(mean value) ID [%] , f , f , f , f0 0 36, f , f , f , , f , f , f , , f , f , f , : volume fraction of steel fiber (%), : Elastic modulus (MPa), : compressive strength of concrete (tested value, MPa), : splitting strength of concrete (MPa), : flexural strength of concrete (MPa) (a) Effect of compressive strength 3.2 쪼갬인장강도 원주형공시체를사용하여수행한쪼갬인장강도시험결과를 Table 7에압축강도시험결과와함께나타내었다. 강섬유로보강되지않은시험체는초기균열의발생과함께파괴에이르는것으로나타났으나강섬유로보강되어있을경우중앙부에균열발생이후균열이확산되며파괴에이르는것으로확인되었다. 이러한현상은섬유의혼입률이높아지면서더확연히나타났으나, 콘크리트의압축강도가증가할수록균열이쉽게확산되지않는것으로나타났다. (b) Effect of Reinforcing Index Fig. 2 Splitting Strength 콘크리트의압축강도가쪼갬인장강도에미치는영향을검토하기위해 Fig. 2에시험결과로나타난콘크리트의압축강도-쪼갬인장강도관계를나타내었다. 강섬유는인장강도의증진에직접적인영향을주게되므로강섬유의혼입량을고려하여나타내었다. Fig. 2(a) 에나타난바와같이초고강도영역에서큰인장강도의증진률을보 초고강도강섬유보강콘크리트의인장강도와압축강도사이의상관관계에관한연구 255

섬유의보강량은식 (1) 에나타난바와같이섬유보강지수 RI를사용하여나타낼수있으며,

3까지는인장강도의증진이선형적으로증가하는것을확인할수있었다. 그러나섬유보강지수가 0.

5 여주지못하고있다. 이는압축강도가높아질수록인장강도의증진률이낮아진다는기존의연구결과또는추정식의형태를확장하여볼수있는가능성을의미한다. 섬유의보강량은식 (1) 에나타난바와같이섬유보강지수 RI를사용하여나타낼수있으며, 섬유보강지수증가에따른쪼갬인장강도의증진에대해 Fig. 2(b) 에따로나타내었다. 섬유보강지수가 0.3까지는인장강도의증진이선형적으로증가하는것을확인할수있었다. 그러나섬유보강지수가 0.3이상일경우섬유의보강이선형적인강도증진에영향을미치는정도가낮은것을확인할수있었다. 따라서강섬유보강초고강도콘크리트의쪼갬인장강도를결정함에있어서콘크리트의압축강도는기존의방식과같은지수함수를사용하고, 섬유보강량의경우 1 차함수또는지수함수의형태로표현할수있을것으로판단된다. 3.3 휨인장강도 강도는파괴계수로표현되어사용되고있다. 섬유보강초고강도콘크리트의파괴계수를평가하기위한 3점휨시험결과를 Fig. 3에나타내었다. 파괴계수또한쪼갬인장강도와유사한증진율을나타내고있는것을확인할수있었다. 강도의절대량은쪼갬인장강도에대해평균적으로 1.55배가크게나타나고있는것을확인할수있었다. Fig. 3(a) 에나타난바와같이콘크리트의압축강도에대해서는쪼갬인장강도와유사한증진률을보이고있는것으로확인되었으나, Fig. 3(b) 에나타난바와같이강섬유의혼입률증가에따른증진률은쪼갬인장강도에비해더큰비율의선형성을보유한것을확인할수있었다. 이는섬유의분산성이거푸집과가까워짐에따라방향성을가지게되어나타나는현상으로생각된다. 22) 4. Database 를통한인장강도의추정 4.1 Database 에따른기존추정식의신뢰성평가 현행설계기준에따르면콘크리트의휨인장강도는쪼갬인장강도와는달리콘크리트구조물의설계에있어서직접적인영향을미치는요소가된다. 이를위해휨인장 넓은범위의콘크리트강도영역에서간단하게사용가능한기계적성질의추정식과응력-변형률관계를도출하기위해본연구에서는별도로수행한실험결과와 Splitting Strength (a) Effect of compressive strength (a) Splitting Strength Splitting Strength (b) Effect of Reinforcing Index Fig. 3 Flexural Strength(Modulus of Rupture) (b) Flexural Strength Fig. 4 Tensile Strength according to the Compressive Strength 256 한국콘크리트학회논문집제 27 권제 3 호 (2015)

6 Table 8 Database Researcher (%) Fiber Type # of specimens splitting Vanderbilt 23) Sarsam 24) Straight Ramirez 25) Pandor 26) Thomas 27) Hook Voo 28) Straight Mansur 29) Hook Narayanan 30) Crimped Oh 31) Hook Kwak 32) Hook Mansur 33) Straight Shende 34) Hook Jijl 35) Crimped Long 36) Straight, Hook Dancygier 37) Hook Ramadoss 38) Crimped Al-Hassani 39) Straight Khalil 40) Hook, Crimped Ozyildirim 41) Straight Murthy 42) Straight Graybeal 43) Straight Meleka 44) Straight Magureanu 45) Straight Arunachalam 46) Straight Tadros 47) flexural : compressive strength of concrete(tested value, MPa), : splitting strength of concrete(mpa), : flexural strength of concrete(mpa), : volume fraction of steel fiber(%), : reinforcing Index Table 9 Statistical Evaluation : previously suggested equations (test value/estimated value) Type Researcher Mean Median Splitting Strength Standard Deviation Variance Coefficient of Variation Carrasquillo 5) Mokhtarzadeh 6) Nihal Arιoglu 7) M.F.M. Zain 8) Oluokun 9) Ahmad 10) ACI ) NZS ) Narayannan 15) Wafa 16) Song 17) Thomas 18) Ramadoss 19) IAE Fiber Effect Cannot Consider Fiber Effect Considering Fiber 초고강도강섬유보강콘크리트의인장강도와압축강도사이의상관관계에관한연구 257

7 Table 9 Statistical Evaluation : previously suggested equations (test value/estimated value) (Continue) Type Researcher Mean Median Flexural Strength Standard Deviation Variance Coefficient of Variation Carrasquillo 5) Burg 13) Khayat 14) Ahmad 10) ACI ) NZS ) Wafa 16) Song 17) Thomas 18) Ramadoss 19) IAE Fiber Effect Cannot Consider Fiber Effect Considering Fiber 함께기수행된재료시험결과들을수집하여추정식을결정하는데에사용하였다. 수집된시험결과는쪼갬인장강도추정을위한시험체 284개, 휨인장강도시험체 265개로구성되어있다. 콘크리트의압축강도범위는 20~134 MPa인것으로나타났으며섬유의혼입량은 0~6% 의부피비인것으로나타났다. 섬유의종류는강섬유로한정하고 Straight, Hooked-end, Crimped로구분하여검토하였다. Table 8에 Database에대한정보를요약하여나타내었으며 Table 9에기존연구자들이제안한추정식들의신뢰성에대해분석하여나타내었다. 본연구에서는평균값, 표준편차, 분산, 변동계수그리고적분절대오차 (Integral Absolute Error, IAE) 를통계지표로사용되었다. 여기서 IAE는다음식을통해결정하였다. 있었다. 이는기존의추정식이섬유의보강효과를너무크게고려하는것으로판단된다. 이러한현상은통계량에서도확인할수있다. Table 9 에서평균값의경우섬유의영향을고려하지않은실험체는모두안전측의추정을하는것으로나타나고있으나, 섬유의영향을고려한추정식에있어서는 Narayannan 15) 과 Ramadoss 19) 의추정식을제외하고는모두불안전측의추정을하고있는것으로확인할수있다. 표준편차와분산에있어서는섬유로보강하지않은추정식이더낮은값을보이는것을확인할수있었으며, IAE 값또한섬유의보강효과를고려한식이상대적으로더낮은값을보이며높은정확도를보유하고있음을확인할수있었다. (2) 여기서 는관측값, 는추정값을의미한다. 통계량분석과함께추정치의분산정도를확인하기위해쪼갬인장강도와휨인장강도의발현정도를콘크리트의압축강도에의거하여 Fig. 4에나타내었다. 압축강도의고강도화가진행됨에따라인장강도의분산정도가커지는것을확인할수있었다. 강섬유보강콘크리트에대한기존연구자들의추정식을 Fig. 4에실험결과와함께나타내었다. 고강도화에따라인장강도의분산정도가높아지는것과같이, 고강도콘크리트에대해서는추정시의오차가커지는것을확인할수있었다. 특히, 100 MPa 이상의압축강도를보유한초고강도영역에서, 섬유의보강정도를고려하지않은추정식의경우모두 ACI에서제시하는설계를위한추정식과같이안전측의추정을하는것으로나타났다. 그러나섬유의보강을고려한추정식의경우불안전측의추정값이나타나는것을확인할수있으며, 이는콘크리트의압축강도가높아지면서더두드러지게나타나는것을확인할수 Integrated Absolute Error [%] (a) Splitting Strength (b) Flexural Strength Fig. 5 IAE distribution with Compressive Strength 258 한국콘크리트학회논문집제 27 권제 3 호 (2015)

8 기존추정식의초고강도섬유보강콘크리트에대한적합성을검토하기위해, 콘크리트의압축강도에의거하여 IAE를검토하였다. 검토대상은 Table 2와 4의섬유보강콘크리트에대한인장강도추정식으로정하였다. 검토결과 Fig. 5에나타난바와같이 100 MPa 이상의압축강도를보유한초고강도콘크리트영역에서 IAE 증가를확인할수있었다. 섬유의영향을고려하지않은추정식의경우높은 IAE 와함께높은증가율을보이고있는것을확인할수있으며, 섬유의영향을보유한경우고강도화에따른유사한증가경향이나타나고있으나일반적으로고강도콘크리트로간주되는 80 MPa 이하의압축강도영역에서는상대적으로낮은 IAE를확인할수있었다. 이는기존의연구결과가 100 MPa 이상의초고강도영역에서수행된실험결과를적용하지않은상태이기때문인것으로판단된다. IAE는오차의절대량의크기를의미하는것이므로, 평균값과함께검토해본결과, 콘크리트의압축강도가 100 MPa 이상일경우현재까지제시되어있는식은사용이어려울것으로판단된다. Table 10 Results of Regression Analysis ID Splitting Strength Flexural Strength R1 R2 Mean S.D IAE Mean S.D IAE Mean S.D IAE Mean S.D IAE R3 Mean S.D IAE Mean S.D IAE : tensile strength of concrete, : Compressive strength of concrete, : Reinforcing Index, S.D : Standard Deviation, IAE : Integrated Absolute Error(%) 4.2 쪼갬인장강도및휨인장강도의비선형회기분석 각추정식들에대한통계치를분석한결과, 대부분의추정식이해당추정식의도출에사용된데이터의범위를벗어날경우큰오차가발생하는것을확인할수있었다. 특히, 섬유의영향을반영하지않을경우오차가크게나타나는것을확인할수있었다. 따라서, 본연구에서는고강도및섬유의보강효과를동시에반영할수있는, 압축강도를기반으로한쪼갬인장강도및휨인장강도의추정식을수집한데이터를기반으로한비선형회기분석을통해도출하였다. 비선형회기분석을통해고강도콘크리트및섬유보강콘크리트에적용이가능한추정식의도출을위해서는주요독립변수의결정과함께기본식의형태를결정해주어야한다. 콘크리트의인장강도에대한기존추정식의형태를검토한결과, 콘크리트압축강도의영향은식 (3) 에나타난바와같이, 압축강도의제곱근또는특정한지수와함께특정상수를곱하여결정할수있는것을확인할수있었다. (3) 여기서, 는콘크리트의쪼갬인장강도, 는콘크리트의압축강도이며, 와 는회기분석에의해도출되는상수이다. 강섬유의영향은일반적으로두가지경우로분류된다. 섬유가보강되지않은콘크리트매트릭스의강도에대한배율이되는경우와섬유의독립적인강도증가분이더해지는경우이다. 후자의경우섬유의보강이되어 spf ck 2 / (0.125 ) 3 frf 1.75 fck RI f f RI Fig. 6 Evaluation of Proposed Model 있지않을때에보강효과가없는상태로만들기가어려우므로본연구에서는고려하지않기로하였다. 이에따라섬유의영향을고려하기위한회기식의형태는다음식 (4) 와같은형태가된다. (4) 여기서, 는식 (1) 을통해결정되는값이다. 기존의추정식은섬유의부피비를사용하는경우가많이있었으나, 섬유의형상비가미치는영향을반영하기위해 를사용하였다. 섬유의보강량이 0일경우괄호내의값이 1이되어야하므로괄호안의식에서상수 는 1로고정하여, 다항식의형태로회기분석을수행하였다. Table 10에식 (3) 과 (4) 의회기분석결과를나타내었다. 특히, 식 (3) 을사용한회기분석은강섬유를보유하지않은경우와강섬유를보유한경우로나누어평가하였다. 회기분석에의해도출된회기식을사용하여쪼갬인장강도와휨인장강도를추정한결과기존추정식에비해높은정확도를가지고있는것을확인할수있었다. Table 10의 R1과 R2의경우압축강도와섬유의영향을별도로고려하지않아높은수준의정확도를기대하기 초고강도강섬유보강콘크리트의인장강도와압축강도사이의상관관계에관한연구 259

9 어려웠으나콘크리트의압축강도와섬유의효과를동시에고려한 R3식을검토한결과기존추정식에비해높은수준의정확도를기대할수있는것을확인할수있었다. 이는기존의추정식들이섬유의보강효과를단순히중첩함에따라발생하는오차를감소시키고초고강도콘크리트의영향을반영해주었기때문인것으로판단된다. 다만 Fig. 6에나타난본연구에서수행된실험결과에서보이는바와같이 200 MPa 급에서쪼갬인장강도의추정이불안전측으로나타나는것을확인할수있는데, 이는 200 MPa 급의콘크리트제작에있어서는 steam curing, 매트릭스구성요소의차이등과같은더욱많은변수가있기때문인것으로판단된다. 따라서본연구결과에서제안된추정식은 150 MPa 이하의콘크리트에대한간접적인장강도추정에사용할수있을것으로판단된다. 5. 결론본연구에서는강섬유로보강된초고강도콘크리트의압축강도와인장강도사이의관계를평가하기위해재료시험을수행하였으며, 기존연구자들의시험결과수집을통해기존추정식들의적합성평가와초고강도영역에서사용가능한인장강도산정식을제안하였다. 본연구의결과를요약하면다음과같다. 1) 초고강도섬유보강콘크리트의쪼갬인장강도시험결과압축강도의증가는인장강도가증가하는직접적인원인인것으로나타났으며, 인장강도의증가비율은압축강도의증가에따라감소하는것으로나타났다. 섬유의보강효과또한인장강도의증진에비례하는것으로나타나고있으나, 그증진률은섬유보강량의증가와함께감소하는것으로나타났다. 2) 초고강도섬유보강콘크리트의휨인장강도시험결과쪼갬인장강도와유사한증진형태를보이고있었다. 그러나평균적으로 1.55배의높은강도를보유하고있었으며, 섬유보강비에대해서는더큰기울기의선형성을가지고있음을확인할수있었다. 3) 기존연구결과를통해수집한쪼갬인장강도및휨인장강도시험결과를기존인장강도추정식을사용하여평가해본결과, 섬유의영향을고려하지않은경우하한치에대한추정을안전하게하는것으로나타났다. 반면섬유의영향을고려한경우섬유의보강효과를과하게간주하는경향이있음이확인되었다. 4) 기존추정식의초고강도영역에서의사용에대한적합성판단을위해통계분석을수행한결과, 섬유의보강정도를고려하는추정식의경우 100 MPa 미만에서는사용하기에큰문제가없는것으로나타났으나, 100 MPa 이상의압축강도영역에서오차의크기가급격히증가하는것을확인할수있었다. 따라서콘크리트의압축강도가 100 MPa 이상일경우현재까지제시되어있는식은사용이어려울것으로판단된다. 5) 본연구에서수행된시험결과와수집된시험결과를바탕으로회기식을도출하였다. 기존의추정식보다높은정확도를가지고있는것으로나타나고있으나, 150 MPa를초과하는콘크리트의경우배합비의다양성과양생방법의다양성에의해그정확도가비교적떨어지는것을확인할수있었다. 따라서, 차후초고강도콘크리트에대한표준화된배합방안이도출되기전까지는배합비의영향이나양생조건등을고려할수있는별도의방안이마련되어야할것으로판단된다. 감사의글 이논문은 2014년도정부 ( 미래창조과학부, 교육부 ) 의재원과한국연구재단의지원을받아수행된기초연구사업임 (No. NRF-2014R1A1A , NRF-2013R1A1A ). References 1. Korea Concrete Institute, Concrete Design Code and Commentary, Kimoondang Publishing Company, Seoul, Korea, 2012, pp KS F 2423, Standard test method for splitting strength of concrete, Korean Agency for Technology and Standards, 2011, pp KS F 2408, Standard test method for flexural strength of concrete, Korean Agency for Technology and Standards, 2010, pp ACI 363. Report on high strength concrete. Report ACI 363R-10, Farmington Hills, MI, American Concrete Institute, 2010, pp Carrasquillo, R. L., Nilson, A. H. and Slate, F. O., Properties of high strength concrete subjected to short-term load, ACI Journal, Vol.78, No.2, 1981, pp Mokhtarzadeh, A. and French, C. Mechanical Properties of High-Strength Concrete with Consideration for Precast Applications, ACI Materials Journal, Vol.97, No.2, Mar. -Apr., 2000, pp Nihal Arιoglu, Z. Canan Girgin, and Ergin Arιoglu, Evaluation of Ratio between Splitting Tensile Strength and Compressive Strength for Concretes up to 120 MPa and its Application in Strength Criterion, ACI Materials Journal, Vol.103, No.1, Jan.-Feb., 2006, pp Zaina, M. F. M., Mahmudb, H. B. and Faizala, Ade Ilhama, M., Prediction of splitting tensile strength of high-performance concrete, Cement and Concrete Research, Vol.32, 2002, pp 한국콘크리트학회논문집제 27 권제 3 호 (2015)

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11 toughness of high performance fiber reinforced concrete, Journal of Engineering Science and Technology, Taylor s University, Vol.7, No.3, 2012, pp Hisham M. Al-Hassani, Wasan Ismail Khalil and Lubna S. Danha, Mechanical Properties of Reactive Powder Concrete (RPC) with Various Steel Fiber and Silica Fume Contents, Eng. & Tech. Journal, Vol.31, Part (A), No.16, 2013, pp Wasan, I. Khalil and Tayfur, Y. R., Flexural Strength of Fibrous Ultra High Performance Reinforced Concrete Beams, ARPN Journal of Engineering and Applied Sciences, Vol.8, No.3, MARCH 2013, pp Celik Ozyildirim, Evaluation of Ultra-High-Performance Fiber-Reinforced Concrete, Virginia Center for Transportation Innovation and Research, FHWA/VCTIR 12-R1, 2011, pp A. Ramachandra Murthy, Nagesh R. Iyer and B.K. Raghu Prasad, Evaluation of mechanical properties for high strength and ultrahigh strength concretes, Advances in Concrete Construction, Vol.1, No.4, 2013, pp Benjamin A. Graybeal, Material Property Characterization of Ultra-High Performance Concrete, Office of Infrastructure Research and Development, Federal Highway Administration, FHWA-HRT , 2006, pp Nageh, N., Meleka, Alaa A., Bashandy, Mohamed A. Arab, Ultra High Strength Concrete Using Economical Materials, International Journal of Current Engineering and Technology, Vol.3, No.2, June 2013, pp Magureanu, C., Sosa, I., Negrutiu, C. and Heghes, B., Physical and mechanical properties of ultra high strength fiber reinforced cementitious composites, Proceedings of FraMCoS-7, May, 2010, pp Arunachalam. K. and Vigneshwari, M., Experimental investigation on ultra high strength concrete containing mineral admixtures under different curing conditions, International Journal of Civil and Structural Engineering, Vol.2, No.1, 2011, pp Maher, K., Tadros, George Morcous, Application of Ultra-High Performance Concrete to Bridge Girders, University of Nebraska-Lincoln, SPR-P1(08)P310, 2009, pp. 76. 요약최근 RPC를활용한초고강도콘크리트가개발되면서 100 MPa 이상의높은압축강도를보유한콘크리트가취성적파괴의방지목적과인장강도증진을위해강섬유를혼입하여사용되고있다. 따라서인장강도의결정이중요하나, 현재초고강도콘크리트영역에서의인장강도추정을위한연구결과가산발적으로만이루어지고있는상황이다. 따라서본연구에서는 80~200 MPa의압축강도를보유한 RPC의재료시험을수행하여압축강도와인장강도의상관관계를검토하였다. 시험결과 100 MPa 이상의압축강도를보유할경우에도보통강도또는고강도콘크리트영역에서의변화경향이유지되고있는것을확인할수있었다. 이에기존연구로부터수집된, 쪼갬인장강도원주형공시체시험결과 284개와 265개의파괴계수시험결과를활용하여기존의추정식들을평가하였다. 평가결과 100 MPa 이상의초고강도콘크리트에서는기존추정식을안전하게사용하기어려운것을확인하였으며, 100 MPa 이상의초고강도콘크리트에도적용가능한회기식을도출하였다. 핵심용어 : 섬유보강초고강도콘크리트, 쪼갬인장강도, 휨인장강도, 회기분석 262 한국콘크리트학회논문집제 27 권제 3 호 (2015)

14.531~539(08-037).fm

14.531~539(08-037).fm G Journal of the Korea Concrete Institute Vol. 20, No. 4, pp. 531~539, August, 2008 š x y w m š gj p { sƒ z 1) * 1) w w Evaluation of Flexural Strength for Normal and High Strength Concrete with Hooked