KR20220118760A - Method And Computer Program For Providing Optimal Mixture of Air entrained Fly Ash Blended Concrete Considering Carbonation Durability And Frost Durability - Google Patents

Abstract

According to the present invention, a program provides information on an air-infused fly ash mixed concrete composition which has the most inexpensive manufacturing costs and is eco-friendly due to small carbon dioxide generation in consideration of carbonation durability and frost durability considering the total costs and a climate change if inputted is information on a composition element mixture range of concrete, a composition element ratio range, compression strength-frost-workability, and carbonation durability, thereby having an advantage of designing air-infused fly ash mixed concrete with low costs and low carbon dioxide without profession knowledge about concrete.

Description

TECHNICAL FIELD [0002] Method and Computer Program For Providing Optimal Mixture of Air entrained Fly Ash Blended Concrete Considering Carbonation Durability And Frost Durability

The present invention relates to a method for optimal design of an air mixed fly ash mixed concrete composition in consideration of carbonation and freeze-thaw and a computer program thereof.

Fly ash, a by-product of thermal power plants, is in increasing demand as a mineral mixture to partially replace cement in the concrete industry. When fly ash is added to replace cement in the manufacture of concrete, it has the advantage of improving the workability of concrete, the aging strength of hardened concrete, and the chloride and acid resistance of concrete, but has the disadvantage of lowering the carbonation durability of concrete. Therefore, in order to use fly ash in concrete manufacturing, various aspects such as mechanical properties, durability, and sustainability of concrete due to the addition of fly ash should be comprehensively considered (Petcherdchoo, 2018).

Since the sustainability of concrete is an important indicator of concrete, many studies are being conducted on it. For example, Kurda et al. (2019) reported that mixing with recycled concrete aggregate and fly ash can reduce the manufacturing cost of concrete and the environmental impact of concrete; Al-Ayish et al. (2018) reported that the addition of fly ash and slag to the manufacture of concrete exposed to a chloride environment can effectively reduce the climatic impact of the manufacture of concrete; Alnahhal et al. (2018) reported that the carbon dioxide emissions of recycled aggregate concrete decreased by about 29% as a result of replacing 30% of cement with supplementary materials in the manufacture of recycled aggregate concrete. See also Teixeira et al. (2019) reported that mixing a small amount of biomass fly ash with coal fly ash in concrete production can achieve the best environmental performance due to their bonding effect. ; Souto-Martinez et al. (2018) reported that the addition of fly ash lowered the initial carbon content and reduced carbon dioxide sequestration. See also Tam et al. (2019) reported that mixing 100% recycled coarse aggregate with 50% fly ash optimizes the environmental impact and mechanical properties of concrete; Liu et al. (2012) confirmed that the optimal binder content for concrete production was 338 kg/m ³ and the optimal replacement rate of fly ash for cement was 50%. Emissions were reported to be 33% and 35% lower, respectively.

Among the preceding results on the sustainability of concrete, there are only a few studies on the optimal design of a sustainable concrete composition. For example, Yeh (2007, 2009) reported the results of optimizing a concrete composition using a neural network and a flattened simplex-centroid method or a genetic algorithm (GA); Cheng et al. (2014) reported the results of designing the optimal composition of concrete with the lowest material cost by combining a genetic algorithm with a support vector machine. Young et al. (2019) reported the results of predicting the strength of concrete based on machine learning methods and optimizing the design of concrete compositions using the MATLAB optimization toolbox; Park (2013) proposed a genetic algorithm for the mixing design of concrete containing recycled aggregate concrete and reported a design method considering the mechanical and durability characteristics desired for concrete. See also Rezaifar et al. (2016) reported the results of optimizing the design of crumb rubber and meta-kaolin mixed concrete; Xuan et al. (2012) reported a method for optimizing a concrete composition combining cemented demolition waste and recycled stone based on the reaction surface method.

However, the composition design method has the following disadvantages.

First, the optimization design method of the preceding studies focuses on the compressive strength of concrete and has limitations in which durability is not considered at all (Cheng et al., 2014; Rezaifar et al., 2016; Xuan et al. ., 2012; Yeh, 2007, 2009; Young et al., 2019). Carbonation constraint in fly ash mixed concrete is a necessary constraint for optimal composition design of sustainable concrete. When the fly ash mixed concrete and the normal concrete have the same compressive strength, the carbonation resistance of the fly ash mixed concrete is lower than that of the general concrete. Therefore, if the fly ash mixed concrete composition is designed only on the basis of compressive strength, the carbonation durability of the concrete made of the composition cannot be guaranteed (Thomas, 2013).

Second, the optimization design method of the preceding studies has limitations in that the effect of global warming on concrete is not considered at all (Cheng et al., 2014; Park, 2013; Rezaifar et al., 2016; Xuan et al., 2012). ; Yeh, 2007, 2009; Young et al., 2019). An increase in atmospheric carbon dioxide concentration and temperature causes global warming, which leads to an increase in the carbonation rate of concrete, which reduces the durability of concrete (Yoon et al., 2007; Papadakis et al., 2002; Papadakis and Tsimas, 2002). . Therefore, for the optimal design of the fly ash mixed concrete composition, the limiting conditions of carbonation combined with global warming must be taken into consideration, thereby solving the global warming problem and producing highly durable concrete.

Third, the optimization design method of the preceding study focused on air-free concrete, but studies on air-entrained concrete are limited. Concrete mixed with air has excellent frost resistance and thawing cycle resistance compared to concrete without air, so it is often used as durable concrete in cold areas.

Therefore, if an optimized design method for air-blended fly ash mixed concrete composition is developed that can compensate for the disadvantages of the preceding studies, it is environmentally friendly by reducing the amount of carbon dioxide induced during concrete production and has excellent durability in response to global warming and cold concrete. is considered to be able to manufacture.

The patents and references mentioned in this specification are hereby incorporated by reference to the same extent as if each publication were individually and expressly specified by reference.

Akhtar, M. N., Akhtar, J., Tarannum, N., 2019. Civ. Eng. J. 5, 1041e1051. Al-Ayish, N., During, O., Malaga, K., Silva, N., Gudmundsson, K., 2018. Nord. Concr. Res. 58, 77e93. Alnahhal, M. F., Alengaram, U. J., Jumaat, M. Z., Abutaha, F., Alqedra, M. A., Nayaka, R. R., 2018. J. Clean. Prod. 203, 822e835. Benazzouk, A., Douzane, O., Mezreb, K., Queneudec, M., 2006. Cement Concr. Compos. 28, 650e657. Burciaga, U.M., Saez, P.V., Ay on, F.J.H., 2019. Emerg. Sci. J. 3, 274e284. Cheng, M.-Y., Prayogo, D., Wu, Y.-W., 2014. J. Comput. Civ. Eng. 28, 1e7. Czarnecki, L., Woyciechowski, P., 2015. Bull. Pol. Acad. Sci. Tech. Sci. 63, 43e54. Heede, P.V.d., Furniere, J., Belie, N.D., 2013. Cement Concr. Compos. 37, 293e303. IPCC, 2014. Future climate changes, risks and impacts. https://ar5-syr.ipcc.ch/topic_futurechanges.php. Accessed 2019.10.30 2019. Kurda, R., Brito, J.d., Silvestre, J.D., 2019. J. Clean. Prod. 226, 642e657. Lam, L., Wong, Y.L., Poon, C.S., 1998. Cement Concr. Res. 28, 271e283. Li, B., Dong, S., Wen, Y., 2013. Appl. Mech. Mater. 353e356, 2769e2773. Lim, C.-H., Yoon, Y.-S., Kim, J.-H., 2004. Cement Concr. Res. 34, 409e420. Liu, R., Durham, S. A., Rens, K. L., Ramaswami, A., 2012. J. Mater. Civ. Eng. 24, 745e753. Mathworks, 2019. www.mathworks.com. Mehta, P.K., Monteiro, P.J.M., 2014. Concrete Microstructures, Properties, and Materials, fourth ed. Mc Graw Hill education, New York. Momtazia, A.S., Tahmouresi, B., Khoshkbijari, R.K., 2016. Civ. Eng. J. 2, 189e196. Mosley, B., Bungey, J., Hulse, R., 2012. Reinforced Concrete Design to Eurocode 2, seventh ed. Palgrave macmillan, UK. Naibaho, A., 2018. Civ. Eng. J. 4, 702e711. Neville, A.M., 1996. Properties of Concrete, fourth and final edition. John widely & sons, London. Oh, B.H., Jang, S.Y., 2004. Cement Concr. Res. 34, 463e480. Papadakis, V. G., Tsimas, S., 2002. Cement Concr. Res. 32, 1525e1532. Papadakis, V. G., Antiohos, S., Tsimas, S., 2002. Cement Concr. Res. 32, 1533e1538. Park, W., 2013. Trans. Can. Soc. Mech. Eng. 37, 345e354. Petcherdchoo, A., 2018. Adv. Mater. Sci. Eng. 2018 Article ID 2793481. Rezaifar, O., Hasanzadeh, M., Gholhaki, M., 2016. Construct. Build. Mater. 123, 59e68. Souto-Martinez, A., Arehart, J. H., Srubar, Wil V., 2018. Energy Build. 167, 301e311. Standardization, E.C.f., 2006. Eurcode Code 2: Design of Concrete Structures. British Standards Institution, UK. Tam, V.W.Y., Le, K.N., Evangelista, A.C.J., Butera, A., Tran, C.N.N., Teara, A., 2019. Manag. 6, 395e405. Teixeira, E. R., Mateus, R., Camoes, A., Branco, F. G., 2019. Construct. Build. Mater. 197, 195e207. Thomas, M., 2013. Supplementary Cementing Materials in Concrete. CRC Press,-Taylor & Francis Group, Boca Raton. Wang, X.-Y., Luan, Y., 2018. Comput. Concr. 21, 419e429. Wong, H.S., Pappas, A.M., Zimmerman, R.W., Buenfeld, N.R., 2011. Cement Concr. Res. 41, 1067e1077. Xiao, R., Ma, Y., Jiang, X., Zhang, M., Zhang, Y., Wang, Y., Huang, B., He, Q., 2020a. J. Clean. Prod. 252, 119610. Xiao, R., Polaczyk, P., Zhang, M., Jiang, X., Zhang, Y., Huang, B., Hu, W., 2020b. Transport Res. Board 2674, 22e32. Xuan, D.X., Houben, L.J.M., Molenaar, A.A.A., Shui, Z.H., 2012. Mater. Struct. 45, 143e151. Yang, K.-H., Jung, Y.-B., Cho, M.-S., Tae, S.-H., 2015. J. Clean. Prod. 103, 774e783. Yeh, I.-C., 2007. Cement Concr. Compos. 29, 193e202. Yeh, I.-C., 2009. Eng. Compute. 25, 179e190. Yoon, I.-S., Copuroglu, O., Park, K.-B., 2007. Atmos. Environ. 41, 7274e7285. Young, B. A., Hall, A., Pilon, L., Gupta, P., Sant, G., 2019. Cement Concr. Res. 115, 379e388. Zhang, P., Li, D., Qiao, Y., Zhang, S., Sun, C., Zhao, T., 2018. J. Mater. Civ. Eng. 30, 1e9.

The present invention is a method that allows users without professional knowledge to optimize and design an air mixed fly ash mixed concrete composition that has carbonation durability and frost durability in consideration of carbonation and freeze-thaw, and minimizes carbon dioxide emissions and has a low total manufacturing cost and a computer program thereof.

Other objects and technical features of the present invention are set forth more specifically by the following detailed description of the invention, claims and drawings.

The present invention provides an optimal design method for an air mixed fly ash mixed concrete composition in consideration of carbonation and freeze thawing,

When the computer runs the program for optimal design of air-entrained fly ash mixed concrete composition,

^{Components ( _ _ _} a component mixing range input window for inputting a lower limit and an upper limit of the component); Component ratio where lower and upper limits of the component ratio can be entered, including water/binder ratio, fly ash/binder ratio, water/solid ratio, aggregate/binder ratio, and sand ratio range input window; Compressive strength-frost-workability input window including a design compressive strength value (MPa) input window at the age of 28 days, a design slump value (mm) input window, and an air mixing amount (%) input window; Service life value (years), environmental temperature value (℃), relative humidity value (%), carbon dioxide concentration (%), cover depth value (mm), and climate change scenarios of Representative Concentration Pathways (RCP) a carbonation durability condition input window capable of inputting a carbonation durability limit condition including a type; Cement (kg/m ³ ), fly ash (kg/m ³ ), water (kg/m ³ ), fine aggregate (kg/m ³ ), coarse aggregate (kg/m ³ ), water reducing agent (kg/m ³ ), and a concrete composition content output window for outputting an optimal content of a fly ash mixed concrete composition containing an air admixture ((kg/m ³ ); a calculation execution button; and a save button; a first step of providing on the screen;

When the component mixing range input window, the component ratio range input window, the compressive strength-frost-workability input window, and the carbonation durability condition input window are all input and the calculation execution button is selected and the calculation is executed,

The program calculates the total cost as an objective function, and uses the input value to limit the compressive strength limit, workability limit, carbonation durability limit, frost durability limit, absolute volume limit, component mixing range limit Calculating the content of cement, fly ash, water, fine aggregate, and coarse aggregate, and the content of water reducing agent and air entraining agent that satisfy the conditions and component ratio constraint conditions,

The content of the cement, fly ash, water, fine aggregate, and coarse aggregate and the content of the water reducing agent and the air admixture have the minimum value of the objective function using a genetic algorithm, and the compressive strength limiting condition, workability limiting condition , carbonation durability limitation condition, frost durability limitation condition, absolute volume limitation condition, component mixing range limitation condition, and component ratio limitation condition are calculated and output to the concrete composition content output window It provides an optimal design method of an air mixed fly ash mixed concrete composition in consideration of carbonation and freeze thawing, including:

In the present invention, if only information on the component mixing range of concrete, component ratio range, compressive strength-frost-workability, and carbonation durability is input, the program takes into account the total cost, carbonation durability and frost durability in consideration of climate change. It has the advantage of being able to design low-cost, low-carbon dioxide air-blended fly ash mixed concrete without concrete expertise as it provides information on the eco-friendly air mixed fly ash mixed concrete composition with the lowest manufacturing cost and low carbon dioxide emission. .

1 shows a flow chart for the calculation of the present invention.
2 shows the carbonation depth of the air-entrained fly ash mixed concrete composition without considering carbonation of the present invention. Panel (a) shows the results of Example 1-1 (Mix 1), panel (b) shows the results of Example 1-2 (Mix 2), and panel (c) shows the results of Example 1-3 (Mix 3) shows the result.
3 shows the carbonation depth of the air mixed fly ash mixed concrete composition considering carbonation of the present invention. Panel (a) shows the results of Example 2-1 (Mix 4), panel (b) shows the results of Example 2-2 (Mix 5), and panel (c) shows the results of Example 2-3 (Mix 6) shows the result.
Figure 4 shows the increase in the carbonation depth according to the climate change of the present invention. Panel (a) shows the increase in carbon dioxide over time in RCP 6.0, panel (b) shows the increase in temperature over time in RCP 6.0, and panel (c) shows carbonation due to climate change (global warming) shows an increase in depth.
5 shows the carbonation depth of the air mixed fly ash mixed concrete composition in consideration of climate change of the present invention. Panel (a) shows the results of Example 3-1 (Mix 7) with an air mixing amount of 3.5%, and panel (b) shows the results of Example 3-2 (Mix 8) with an air mixing amount of 5% and panel (c) shows the result of Example 3-3 (Mix 9) in which the air mixing amount was 6%.
6 shows the carbonation depth of the high-strength air-entrained fly ash mixed concrete of the present invention. Panel (a) shows the results of Example 4-1 (Mix 10) with an air mixing amount of 3.5%, and panel (b) shows the results of Example 4-2 (Mix 11) with an air mixing amount of 5% and panel (c) shows the result of Example 4-3 (Mix 12) in which the air mixing amount was 6%.
7 shows the change in the total cost according to the change in the amount of air entrained in the present invention. Panel (a) shows the total cost according to the compressive strength of air mixed fly ash mixed concrete with an air mixing amount of 3.5%, and panel (b) shows the total cost according to the compressive strength of air mixed fly ash mixed concrete with an air mixing amount of 5%. and panel (c) shows the total cost according to the compressive strength of air mixed fly ash mixed concrete with an air mixing amount of 6%.
8 shows the result of inputting the input value into the input window of the optimal design program of the air mixed fly ash mixed concrete composition of the present invention.
Figure 9 shows the output of the calculated result value by executing the optimal design program of the air mixed fly ash mixed concrete composition of the present invention.
Figure 10 shows the output result of converting the calculated result value to Excel by executing the optimal design program of the air mixed fly ash mixed concrete composition of the present invention.

The present invention relates to an optimal design method of an air mixed fly ash mixed concrete composition considering carbonation and freeze ^- thaw, when the optimal design program of the air mixed fly ash mixed concrete composition is executed in the computer, the program is , Fly ash (kg/m ³ ), water (kg/m ³ ), coarse aggregate (kg/m ³ ) and fine aggregate (kg/m ³ ) The lower limit of the composition of the component (kg/m 3 ) and a component mixing range input window for inputting an upper limit; Component ratio where lower and upper limits of the component ratio can be entered, including water/binder ratio, fly ash/binder ratio, water/solid ratio, aggregate/binder ratio, and sand ratio range input window; Compressive strength-frost-workability input window including a design compressive strength value (MPa) input window at the age of 28 days, a design slump value (mm) input window, and an air mixing amount (%) input window; Service life value (years), environmental temperature value (℃), relative humidity value (%), carbon dioxide concentration (%), cover depth value (mm), and climate change scenarios of Representative Concentration Pathways (RCP) a carbonation durability condition input window capable of inputting a carbonation durability limit condition including a type; Cement (kg/m ³ ), fly ash (kg/m ³ ), water (kg/m ³ ), fine aggregate (kg/m ³ ), coarse aggregate (kg/m ³ ), water reducing agent (kg/m ³ ), and a concrete composition content output window for outputting an optimal content of a fly ash mixed concrete composition containing an air admixture ((kg/m ³ ); a calculation execution button; and a save button; a first step of providing on the screen; When the component mixing range input window, the component ratio range input window, the compressive strength-frost-workability input window, and the carbonation durability condition input window are all input and the calculation execution button is selected and the calculation is executed, the program is the objective function Calculate the total cost, and use the input values to limit the compressive strength, workability, carbonation durability, frost durability, absolute volume, component mixing range, and component ratio Calculate the content of cement, fly ash, water, fine aggregate, and coarse aggregate that satisfy the limiting conditions, and the content of the water reducing agent and air entraining agent, wherein the content of the cement, fly ash, water, fine aggregate, and coarse aggregate, and the water reducing agent and air The content of the admixture has a minimum value of the objective function using a genetic algorithm, and the compressive strength limiting condition, workability limitation condition, carbonation durability limitation condition, frost durability limitation condition, absolute volume limitation condition, component formulation A second step of calculating an optimal content value that satisfies the range limitation condition and the component ratio limitation condition and outputting it to the concrete composition content output window; It provides an optimal design method.

The objective function and constraint for calculating the calculation result of the present invention will be described as follows.

The objective function of the present invention is the following Equations 1 to 3:

(The above COST means the total cost of concrete; COST _M means the material cost of concrete; COST _CO2 means the cost of CO ₂ emission of concrete.)

(COST _M in Equation 2 means the material cost of concrete; m _i means the mass of cement, fly ash, water, fine aggregate, coarse aggregate, water reducing agent and air-entraining agent; Pr _i is the amount of individual components of concrete means the price.)

(COST _CO2 in Equation 3 means the cost of CO ₂ emission of concrete; Pr _CO2 means the unit price of CO ₂ (Pr _CO2 is set to NT $885.496/ton (Inc, 2019)) CO _2i is concrete refers to the CO2 emissions _of individual components of

: It is characterized in that it is calculated by .

The compressive strength limitation condition means that the design compressive strength value at the age of 28 days is greater than or equal to the actual compressive strength value at the age of 28 days, and the design compressive strength value is the following Equation 4:

는 콘크리트의 효율적인 물/바인더 비율을 의미한다.)(f _c in Equation 4 refers to compressive strength; W refers to the mass of water; C refers to the mass of cement; FA refers to the mass of fly ash. In addition, V _air is the mixed air of (the unit of V _air is %);

is the effective water/binder ratio of concrete.)

: It is characterized in that it is calculated by .

The workability limitation condition means that the design slump value is greater than or equal to the actual slump value, and the slump value is Equation 5:

는 물/바인더 비율을 의미하며;

는 전체 골재에 대한 모래의 비율을 의미하며,

는 플라이 애쉬 대체 비율을 의미하며; 1+0.03V_air는 혼입된 공기로 인한 슬럼프 증가를 의미한다.)(SD in Equation 5 means the mass of sand; CA means the mass of coarse aggregate; SP means the mass of superplasticizer; C means the mass of cement and FA means the mass of fly ash.

means the water/binder ratio;

is the ratio of sand to total aggregate,

denotes the fly ash replacement ratio; 1+0.03V _air means an increase in slump due to entrained air.)

: It is characterized in that it is calculated by .

The carbonation durability limiting condition means that the carbonation depth is smaller than the cover depth, and the carbonation depth is the following Equations 8 and 9:

)를 의미하며; β는 이산화탄소 확산의 활성화 에너지(β=4300)를 의미하며; T_ref는 기준 온도(293K)를 의미하며; T는 환경 온도를 의미하며; (V_air-2)^*0.01은 혼입된 공기로 인해 증가하는 콘크리트 다공성을 의미한다.)(χ _c in Equation 8 or 9 means carbonation depth; D means carbon dioxide diffusivity of concrete; [CO ₂ ] ₀ means carbon dioxide concentration; t means exposure time; ρ _c denotes the density of cement; ρ _w denotes the density of water; RH denotes the relative humidity of exposure; α _H denotes the degree of hydration (

) means; β denotes the activation energy of carbon dioxide diffusion (β=4300); T _ref means the reference temperature (293K); T stands for environmental temperature; (V _air -2) ^* 0.01 means concrete porosity increased due to entrained air.)

: It is characterized in that it is calculated by .

The frost durability limit condition is that the damage to concrete caused by repeated freezing and thawing is smaller than the degree of concrete damage of the ACI code according to the value entered in the air mixing amount (%) input window, and the compressive strength limit condition is satisfied. characterized in that

The absolute volume limiting condition means that the sum of the volumes of the concrete components is equal to the value obtained by subtracting the air mixing amount (%) from 1m ³ , and the absolute volume limiting condition is the following Equation 10:

(m _i in Equation 10 refers to the mass of the component; ρ _i refers to the density of the component; V _air refers to the amount of air mixed (%).)

: It is characterized in that it is calculated by .

The component mixing range limiting condition means that the amount of addition of the component corresponds to between the component mixing lower limit and the upper limit, and the component ratio limiting condition is that the mixing ratio of the component is the It is characterized in that it falls between the lower limit and the upper limit of the component ratio.

The content of the water reducing agent is the following Equation 6:

(The above SP means the mass of the water reducing agent; W means the mass of water; C means the mass of cement; FA means the mass of fly ash.)

: It is characterized in that it is calculated by .

The content of the air mixing agent is the following Equation 7:

(The AE means the content of the air admixture; the V _air means the air content (%); C means the mass of cement; FA means the mass of fly ash.)

: It is characterized in that it is calculated by .

The present invention provides a computer-readable recording medium characterized in that the optimum design method of the air mixed fly ash mixed concrete composition in consideration of the carbonation and freeze-thaw is recorded as a program that can be executed by a computer.

In the present invention, the subject performing the optimal design method of the air mixed fly ash mixed concrete composition in consideration of carbonation and freezing and thawing may be an overall system running the program. The system may be a controller or a processor that generally controls a system or apparatus for driving a program. Therefore, the optimal design method of the air mixed fly ash mixed concrete composition in consideration of carbonation and freezing and thawing of the present invention is composed of a program that is a kind of software, and the program can be executed in a system, computer or processor.

In the present invention, the subject performing the optimal design method of the air mixed fly ash mixed concrete composition in consideration of carbonation and freeze-thaw may be various computer devices. The computer device may be a computer, a controller of the computer, or a processor.

Hereinafter, the present invention will be described in detail by way of Examples.

Example

1. Optimal design method of air-entrained fly ash mixed concrete composition

1) objective function

The present invention is an air-entrained fly ash-blended concrete mixture having low carbon dioxide emissions, low manufacturing cost, eco-friendly, carbonation durability optimized for global warming, and strong frost durability against cold It's about designing. Since the unit for the emission of carbon dioxide and the unit for the manufacturing cost of concrete are different from each other, the cost for carbon was converted using the unit of carbon dioxide emission. The aim function of the present invention is set as the total cost, and the total cost is equal to the material cost plus the carbon dioxide emission cost (refer to Equation 1).

[Equation 1]

COST in Equation 1 means the total cost of concrete; COST _M means the material cost of concrete; COST _CO2 means the cost _of CO2 emission of concrete.

In detail, the material cost of the concrete means the sum of the individual costs of the concrete components (refer to Equation 2).

[Equation 2]

m _i in Equation 2 means the mass of cement, fly ash, water, fine aggregate, coarse aggregate, water reducing agent, and air mixing agent; Pr _i means the unit price of individual components of concrete.

In addition, the CO ₂ emission cost of the present invention is equal to the value obtained by multiplying the CO ₂ emission by the unit price of CO ₂ (see Equation 3).

[Equation 3]

Pr _CO2 in Equation 3 means the unit price of CO ₂ (Pr _CO2 is set to NT $885.496/ton (Inc, 2019)), and CO _2i means CO ₂ emissions of individual components of concrete. For reference, the Pr _CO2 is set to NT $885.496/ton (Inc, 2019).

Table 1 below shows the unit cost and unit CO ₂ emissions of concrete components (Yang et al., 2015; Yeh, 2007).

The design of concrete compositions includes compressive strength, workability, carbonation durability, frost durability, absolute volume, component range as constraints. range) and component ratios (Yeh, 2007; Young et al., 2019).

Hereinafter, the limiting conditions of the design method for the concrete composition of the present invention will be described in detail.

2) Compressive strength limiting conditions

The compressive strength constraint of the present invention means that the real compressive strength at a specific age is greater than or equal to the design compressive strength.

The compressive strength of concrete is rapidly formed at the beginning of molding and its strength continues to increase even after 28 days of age, but the hydration rate and strength increase rate are very slow. In the present invention, the compressive strength at the age of 28 days was used as the design compressive strength.

The compressive strength of air-entrained concrete is characterized by a decrease in proportion to the amount of air mixed (A.M. Neville, 1996; Lam et al., 1998). According to the results of previous studies, fly ash mixed concretes with various water-to-binder ratios, fly ash content, air content and curing age were prepared and As a result of experimentally examining the compressive strength for the Thomas (2013); Neville (1996)).

Based on the experimental results, the compressive strength of the air mixed fly ash mixed concrete having an age of 28 days may be determined as shown in Equation 4 below.

[Equation 4]

는 콘크리트의 효율적인 물/바인더 비율을 의미한다. 상기 V_air의 계수 0.05는 혼입된 공기의 함량이 1% 증가하면 압축 강도가 5% 감소한다는 것을 의미한다(AMNeville, 1996; Mehta and Monteiro, 2014).f _c in Equation 4 means compressive strength; W means the mass of water; C means the mass of cement; FA stands for the mass of fly ash. In addition, the V _air means the content of the mixed air (unit of V _air is %);

is the effective water/binder ratio of concrete. The coefficient of V _air of 0.05 means that when the content of air mixed is increased by 1%, the compressive strength decreases by 5% (AMNeville, 1996; Mehta and Monteiro, 2014).

3) Workability Restrictions

The workability constraint of the present invention means that the real slump of concrete must be greater than or equal to the design slump (Mehta and Monteiro, 2014). Previous results have shown that water-to-binder ratio, water ratio, sand ratio, fly ash replacement level and superplasticizer content are mutually exclusive. The slump was experimentally measured for different fly ash mixed concrete 104 mixing ratios, and the effect of the air admixture on the slump was experimentally analyzed (Lim et al. (2004); Benazzouk et al. (2006); Li et al. al. (2013)).

The slump for the air mixed fly ash mixed concrete of the present invention is explained by Equation 5 based on the experimental results.

[Equation 5]

는 물/바인더 비율을 의미하며;

는 전체 골재에 대한 모래의 비율을 의미하며,

는 플라이 애쉬 대체 비율을 의미하며; 1+0.03V_air는 혼입된 공기로 인한 슬럼프 증가를 의미한다.SD in Equation 5 means the mass of sand; CA means the mass of coarse aggregate; SP stands for the mass of superplasticizer; C means the mass of cement; FA stands for the mass of fly ash.

means the water/binder ratio;

is the ratio of sand to total aggregate,

denotes the fly ash replacement ratio; 1+0.03V _air means increased slump due to entrained air.

According to previous results, as the water/binder ratio increases, the mass of the water reducing agent decreases (Lim et al. (2004); Thomas (2013)). Therefore, the mass of the water reducing agent of the present invention may be determined by the water/binder ratio (Equation 6).

[Equation 6]

The mass of the air entrainer of the present invention is determined as a function of air content, binder content and fly ash replacement ratio. According to the previous results, it was experimentally proven that the mass of the air admixture increases when the content of the binder and target air is increased, and the mass of the air admixture also increases as the fly ash content increases (Young et al. (Young et al. (Young et al. 2019); Thomas (2013), Li et al. (2013); Zhang et al. (2018)).

Based on the experimental results, the mass of the air mixing agent may be determined as in Equation 7 below.

[Equation 7]

은 플라이 애시의 추가로 인한 공기 혼입 함량의 증가를 의미한다(Thomas, 2013).The AE means the content of the air entraining agent; The V _air means the amount of air mixed (%); C means the mass of cement; FA stands for the mass of fly ash. In addition, 0:00005 * V _air * (C + FA) in Equation 7 means that the content of the air admixture increases when the content of the binder and air increases, and the

indicates an increase in the air entrainment content due to the addition of fly ash (Thomas, 2013).

4) Carbonation durability limiting conditions

The addition of fly ash to the concrete composition increases the carbonation depth of the concrete, which leads to a decrease in carbonation durability (Thomas, 2013). Therefore, in the present invention, the carbonation durability was used as a limiting condition for the optimal design method of the concrete composition. The carbonation durability limiting condition of the present invention means that the carbonation depth of the concrete must be lower than the cover depth. Papadakis et al. (2002) and Papadakis and Tsimas (2002) experimentally analyzed the carbonation and exposure conditions of a concrete composition using a cement substitute according to the substitute material, and calculated the diffusion-based equation for the carbonation depth of the fly ash mixed concrete by Equation 8 and 9 have been proposed.

[Equation 8]

[Equation 9]

(Oh and Jang, 2004))를 의미하며; β는 이산화탄소 확산의 활성화 에너지(β=4300)를 의미하며; T_ref는 기준 온도(293K)를 의미하며; T는 환경 온도를 의미하며; (V_air-2)^*0.01은 혼입된 공기(공기 비혼입 콘크리트의 경우 포획된 공기의 함량을 2%로 가정함(Czarnecki and Woyciechowski, 2015; Heede et al., 2013; Wong et al., 2011))로 인해 증가하는 콘크리트 다공성을 의미한다. 상기 수학식 8 및 9에 따르면 공기 혼입량이 증가하게 되면 이산화탄소의 확산성과 콘크리트의 탄산화 깊이는 증가하게 되고 탄산화율 또한 이산화탄소 농도와 온도에 비례하여 증가하게 된다(Czarnecki and Woyciechowski, 2015; Wong et al., 2011).χ _c in Equation 8 or 9 means carbonation depth; D means the carbon dioxide diffusivity of concrete; [CO ₂ ] ₀ means the concentration of carbon dioxide; t means exposure time; ρ _c means the density of cement; ρ _w means the density of water. Also, the RH means the relative humidity of the exposure; α _H is the degree of hydration (

(Oh and Jang, 2004)); β denotes the activation energy of carbon dioxide diffusion (β=4300); T _ref means the reference temperature (293K); T stands for environmental temperature; (V _air -2) ^* 0.01 is entrained air (in the case of non-air-entrained concrete, the content of trapped air is assumed to be 2% (Czarnecki and Woyciechowski, 2015; Heede et al., 2013; Wong et al., 2011) )) due to increased concrete porosity. According to Equations 8 and 9, when the air mixing amount increases, the diffusivity of carbon dioxide and the carbonation depth of concrete increase, and the carbonation rate also increases in proportion to the carbon dioxide concentration and temperature (Czarnecki and Woyciechowski, 2015; Wong et al. , 2011).

5) Frost Endurance Limitations

When freezing and thawing are repeated, surface scaling and internal cracking of concrete are confirmed. Durability against this phenomenon is called frost durability, and entrained air is required to confirm the frost durability. The frost durability limiting condition of the present invention means that the damage to concrete due to repeated freezing and thawing must be less than the specified specification. According to the ACI code, for a coarse aggregate maximum size of 19 mm, the recommended entrained air content is 3.5% for mild exposure; 5% for moderate exposure; It is found to be 6% for severe exposure (Mehta and Monteiro, 2014; Thomas, 2013). Based on this, the frost durability of the present invention was determined depending on whether the recommended air content and compressive strength of the concrete were satisfied.

6) Absolute Volume Constraints

The absolute volume limiting condition of the present invention means that the sum of the concrete component volumes is equal to 1 m ³ minus the volume of entrained air. The absolute volume limiting condition is expressed as Equation 10 below.

[Equation 10]

mi in Equation 10 means the mass of the component; ρi means the density of the component; V _air means the amount of air mixed (%).

7) Component Range Constraints and Component Ratio Constraints

The component range constraint of the present invention is that of concrete composition components including cement, fly ash, water, fine aggregate and coarse aggregate. It means that the content should be within the upper and lower limits of Table 2 below (see Table 2). In addition, the component ratio constraint of the present invention is a water-to-binder ratio, a fly ash-to-binder ratio, a sand ratio, and an aggregate/binder ratio. -to-binder ratio) and the ratio between the components of the concrete composition including the water-to-solid ratio should be located within the upper and lower limits of Table 2 below (Thomas, 2013; Yeh) , 2007, 2009).

8) Summary of the proposed model

The optimization of the air-entrained fly ash mixed concrete composition of the present invention consists of an objective function and a limiting condition. The objective function means the total cost including the cost of concrete material and carbon dioxide emission (refer to Equations 1 to 3), and the limiting conditions are compressive strength (refer to Equation 4), workability (refer to Equations 5 to 7), and carbonation durability (see Equations 8 to 9), frost durability, absolute volume (see Equation 10), component ranges and component ratios. The optimization of the air-entrained fly ash mixed concrete composition of the present invention was performed using a genetic algorithm (GA) toolbox of MATLAB (Mathworks, 2019). The genetic algorithm is an evolutionary computing algorithm using artificial intelligence technology (Mathworks, 2019). The genetic algorithm mimics the theory of biological evolution, and is an algorithm that mimics adding or deleting genetic traits and maintaining them in order to adapt to the environment. These genetic algorithms are widely used for the determination and optimization of solutions and include crossovers and mutations at the most critical steps.

1 shows the calculation sequence of the present invention. The genetic algorithm fitness function is the total cost, which is the cost of the material plus the cost of carbon dioxide emissions. The property evaluation model of the present invention includes a compressive strength model, a slump model, and a carbonation model in consideration of global warming. The limiting conditions of the present invention include mechanical property limiting conditions, workability limiting conditions, service life limiting conditions, absolute volume limiting conditions, constraint conditions for limiting components, and constraint conditions for component ratios.

The method proposed in the present invention can be applied to concrete containing various types of fly ash, and the details thereof are as follows.

First, the fly ash of the present invention is divided into class C type and class F type fly ash, and the types affect mechanical properties of concrete such as compressive strength, workability and carbonation durability. The present invention relates mainly to the optimal design of air-entrained concrete containing class F fly ash corresponding to low calcium fly ash.

In order to apply the method of the present invention to the optimal design of concrete containing the class C-type fly ash, a compressive strength model (Equation 4), a workability model (Equations 5 to 7), and a carbonation model (Equation 8 and Math It is judged that the performance evaluation model as in Equation 9) should be modified to fit the class C type fly ash and the genetic algorithm should be applied.

Second, when the optimization design method of the air mixed fly ash mixed concrete composition of the present invention is applied to various types of fly ash, the compressive strength model, workability model, carbonation model, frost durability requirements and It is judged that the optimal design is possible only by modifying the same performance evaluation model. Therefore, it is judged that the present invention can be applied as a general method for optimal mixing design of mixed concrete including various types of fly ash.

2. Examples

In an embodiment of the present invention, the results of designing a fly ash mixed concrete composition including various types of air mixed according to carbonation and global warming are presented. The maximum size of the coarse aggregate was assumed to be 19 mm, and the air mixing amount was set as follows according to the design code. The recommended air entrainment for the hardness exposure of the present invention is 3.5%; The recommended air entrainment for moderate exposure is 5%; The recommended air entrainment for severe exposure is 6% (Mehta and Monteiro, 2014; Mosley et al., 2012; Standardization, 2006).

In the present invention, 30 MPa was used as the minimum design strength in consideration of carbonation durability and frost durability, and the covering depth was assumed to be 25 mm (Mehta and Monteiro, 2014; Standardization, 2006). Also, the required slump was set to 180 mm; The carbon dioxide concentration was set at 0.038%; Relative humidity was set at 65%; The temperature was set at 15° C.; Lifespan is set to 50 years.

Table 3 below shows the conditions of Examples of the present invention.

design compressive strength
(design compressive strength) compressive strength
(compressive strength) Carbonation Durability
(carbonation durability) Global Warming
(global warming) Example 1
(case 1) 30MPa Yes No No Example 2
(case 2) 30MPa Yes Yes No Example 3
(case 3) 30MPa Yes Yes Yes Example 4
(case 4) 45 MPa Yes Yes Yes

The above Example 1 (case 1) is for air mixed fly ash mixed concrete considering only compressive strength; The practical example 2 (Case 2) relates to air mixed fly ash mixed concrete in consideration of compressive strength and carbonation durability; The above Example 3 (Case 3) is for the air mixed fly ash mixed concrete considering the compressive strength (30 MPa) to which carbonization and global warming are applied; Example 4 (Case 4) relates to air mixed fly ash mixed concrete considering high-strength compressive strength (45 MPa) to which carbonation and global warming are applied. The design compressive strength of Examples 1 to 3 was 30 MPa, and the design compressive strength of Example 4 was 45 MPa. A total of 12 types of air mixed fly ash mixed concrete compositions (Examples 1-1, 1-2, 1-3, 2-1, 2-2, 2- 3, 3-1, 3-2, 3-3, 4-1, 4-2, and 4-3) were designed and analyzed. Since the design compressive strength of 30 MPa was selected according to the design code, in the case of a concrete structure exposed to moderate humidity, it is determined that the minimum design compressive strength to achieve carbonation durability and frost durability is 30 MPa (Mosley et al., 2012; Standardization). , 2006). In the present invention, a design compressive strength of 45 MPa was selected as a representative value of high-strength concrete. The above example is to show the individual effects of carbonation durability, global warming, and design strength on the optimal design of the air mixed fly ash mixed concrete composition. By comparing Example 1 and Example 2, the effect of carbonation durability can be confirmed. there is; Comparative analysis of Example 2 and Example 3 can confirm the effect of global warming; Comparative analysis of Example 3 and Example 4 confirms the influence of the design compressive strength.

1) Design of fly ash mixed concrete composition without considering carbonation durability

Table 4 shows the composition of the air mixed fly ash mixed concrete mixture without considering the carbonation durability, and Table 5 shows the performance evaluation results for the air mixed fly ash mixed concrete of Examples 1-1, 1-2, and 1-3 shows In Examples 1-1, 1-2, and 1-3, the mixing amount of air was 3.5%, 5%, and 6%, respectively.

Example 1-1
(Mix 1) Example 1-2
(Mix 2) Examples 1-3
(Mix 3) cement (kg/m ³ ) 263.44 280.87 294.45 fly ash (kg/m ³ ) 87.81 93.62 98.15 water (kg/m ³ ) 166.38 163.78 162.06 fine aggregate (kg/m ³ ) 691.42 669.11 653.27 coarse aggregate (kg/m ³ ) 1037.13 1003.67 979.91 superplasticizer (kg/m ³ ) 0.85 2.20 3.11 air-entraining agent (kg/m ³ ) 0.11 0.17 0.22

Example 1-1
(Mix 1) Example 1-2
(Mix 2) Examples 1-3
(Mix 3) compressive strength(MPa) 30.00 30.00 30.00 slump(mm) 207.39 226.37 239.58 entrained air content (%) 3.5 5 6 carbonation depth (mm) 28.33 30.95 32.45 total cost($NT/m ³ ) 1338.53 1417.66 1476.71 water to binder ratio 0.47 0.44 0.41 fly ash replacement ratio 0.25 0.25 0.25

According to the experimental results, it was confirmed that in Examples 1-1, 1-2, and 1-3, the binder content and total cost increased, while the water/binder ratio decreased; It is confirmed that the same design compressive strength and actual compressive strength are the same as 30 MPa; It is confirmed that the actual slump value (207.39 mm, 226.37 mm, or 239.58 mm) has a higher value than the required slump value (180 mm). In addition, it is confirmed that the fly ash/binder ratio is also the same as the upper limit of 0.25. The upper limit of the ratio is set because the price of fly ash is much cheaper than that of cement, and when the actual compressive strength (30 MPa) is fixed, it is determined that the cost of concrete also increases as the content of air mixed increases.

2 shows the carbonation depths of Examples 1-1, 1-2, and 1-3 calculated based on the carbonation model of the present invention. As the amount of air mixed increases, the carbon dioxide diffusivity of the concrete increases, which leads to an increase in the carbonation depth. After 50 years of service life, the carbonation depth is found to be greater than the cover depth (25 mm). That is, Examples 1-1, 1-2, and 1-3 are conditions that cannot satisfy the carbonation durability requirements, so when designing a mixture of air mixed fly ash mixed concrete, the limiting conditions of carbonation durability must be considered. . The results of the present invention are supported by the results of Czarnecki and Woyciechowski (2015) by Czarnecki and Woyciechowski (2015) that Czarnecki and Woyciechowski (2015) found that air-entrained concrete has a greater carbonation depth than air-entrained concrete.

2) Design of fly ash mixed concrete mixture considering carbonation durability

In the present invention, an air mixed fly ash mixed concrete composition was designed considering carbonation durability as a limiting condition.

Table 6 shows the composition of the examples of the air mixed fly ash mixed concrete composition calculated by the genetic algorithm in consideration of the carbonation durability of the present invention, and Table 7 shows the performance evaluation results of Examples 2-1, 2-2, and 2-3 shows In Examples 2-1, 2-2, and 2-3, the air mixing amounts were 3.5%, 5%, and 6%, respectively.

Example 2-1
(Mix 4) Example 2-2
(Mix 5) Example 2-3
(Mix 6) cement (kg/m ³ ) 286.51 325.52 353.73 fly ash (kg/m ³ ) 95.50 108.51 117.91 water (kg/m ³ ) 166.83 163.85 162.21 fine aggregate (kg/m ³ ) 679.11 645.65 622.39 coarse aggregate (kg/m ³ ) 1018.66 968.48 933.58 superplasticizer (kg/m ³ ) 2.27 4.42 5.67 air-entraining agent (kg/m ³ ) 0.12 0.20 0.26

Example 2-1
(Mix 4) Example 2-2
(Mix 5) Example 2-3
(Mix 6) compressive strength(MPa) 33.16 35.76 37.30 slump(mm) 218.28 244.44 260.58 entrained air content (%) 3.5 5 6 carbonation depth (mm) 25.00 25.00 25.00 total cost($NT/m ³ ) 1442.46 1606.19 1717.57 water to binder ratio 0.44 0.38 0.34 fly ash replacement ratio 0.25 0.25 0.25

The moisture content of Examples 2-1, 2-2, and 2-3 was confirmed to be similar to that of Examples 1-1, 1-2, and 1-3, and the binder content of Examples 1-1, 1- 2, and higher than 1-3. The actual compressive strengths (33.16 MPa, 35.76 MPa, 37.30 MPa) of Examples 2-1, 2-2, and 2-3 are the design strength and Examples 1-1, 1-2, and 1- It is confirmed to be higher than the compressive strength of 3 (30 MPa). The above result means that carbonation durability acted as a decisive factor in the composition design of Examples 2-1, 2-2, and 2-3. According to the result of FIG. 3, it is confirmed that the carbonation depth (25 mm) of Examples 2-1, 2-2, and 2-3 is the same as the coating depth (25 mm). In addition, it is confirmed that Example 1-1 and Example 2-1 have the same air mixing amount (3.5%), but the compressive strength of Example 2-1 has a larger value than that of Example 1-1.

As a result, Example 2 has increased compressive strength compared to Example 1, and it is determined that the cost is also increased. High-strength concrete contains more binder than general-strength concrete, so material cost and carbon dioxide emission cost increase (Yeh., 2007, 2009). Therefore, the cost of Examples 2-2 and 2-3 is determined to be higher than the cost of Examples 1-2 and 1-3, respectively.

3) Design of fly ash mixed concrete mixture considering global warming effect

In the above example, the carbon dioxide concentration was estimated as a limiting condition. However, as suggested by the Intergovernmental Panel on Climate Change (IPCC), carbon dioxide concentration and global temperature increase every year (IPCC, 2014). Accordingly, the IPCC proposed Representative Concentration Pathways (RCP) 8.5, RCP 6.0, RCP 4.5 and RCP 2.6 as climate change scenarios. As the number of the RCP increases, it means the severity of global warming. In the present invention, a fly ash mixed concrete mixture design was performed by applying the RCP 6.0 global warming scenario.

와 시간 평균 온도 증가

를 사용하여 탄산화 깊이를 산출하였다(Wang and Luan, 2018). 도 4의 패널(c)는 기후 변화가 고려된 경우와 기후 변화가 고려되지 않은 경우의 탄산화 깊이를 산출결과를 보여준다. 상기 결과에 따르면 온도가 상승함에 따라 콘크리트의 이산화탄소 확산성이 증가하고 이는 탄산화율의 증가로 이어진다. 또한 이산화탄소 농도의 증가에 따라 이산화탄소의 가스농도 기울기가 증가하므로 탄산화 속도가 향상되는 것으로 확인된다. 따라서 본 발명의 RCP 6.0 시나리오가 고려된 콘크리트의 탄산화 깊이는 피복 깊이보다 높게 된다. 상기 결과는 이산화탄소 농도와 온도의 증가가 콘크리트의 탄산화 깊이를 증가시킨다는 선행연구결과에 의해 지지된다(Yoon et al. 2007). Figure 4 shows the increasing carbon dioxide concentration and global temperature in RCP 6.0 of the present invention. In the present invention, in order to consider the climate change, the time average carbon dioxide concentration

with time average temperature increase

was used to calculate the carbonation depth (Wang and Luan, 2018). Panel (c) of FIG. 4 shows the results of calculating the carbonation depth when climate change is considered and when climate change is not considered. According to the above results, as the temperature increases, the carbon dioxide diffusivity of concrete increases, which leads to an increase in the carbonation rate. In addition, it is confirmed that the carbonation rate is improved because the gradient of the gas concentration of carbon dioxide increases with the increase of the carbon dioxide concentration. Therefore, the carbonation depth of the concrete considering the RCP 6.0 scenario of the present invention is higher than the covering depth. This result is supported by the results of previous studies that an increase in carbon dioxide concentration and temperature increases the carbonation depth of concrete (Yoon et al. 2007).

The carbonation model of the present invention (Equation 9) takes into account the effect of global warming on carbonation depth and the genetic algorithm of the present invention determines the optimal air-entrained fly ash concrete composition for the climate change scenario RCP 6.0. As shown in Tables 8 and 9, when climate change is taken into account, the binder content of concrete increases and the compressive strength increases. According to the result of FIG. 5, it was confirmed that the carbonation depth of Examples 3-1 (Mix 7), 3-2 (Mix 8) and 3-3 (Mix 9) was the same as the coating depth. This means that in the case of Examples 3-1, 3-2, and 3-3, the requirement of carbonation durability is satisfied even if a climate change occurs according to the above scenario.

Example 3-1
(Mix 7) Example 3-2
(Mix 8) Example 3-3
(Mix 9) cement (kg/m ³ ) 303.25 345.03 375.30 fly ash (kg/m ³ ) 101.08 115.01 125.10 water (kg/m ³ ) 166.40 163.91 162.29 fine aggregate (kg/m ³ ) 670.27 635.52 611.29 coarse aggregate (kg/m ³ ) 1005.41 953.29 916.94 superplasticizer (kg/m ³ ) 3.16 5.21 0.21 air-entraining agent (kg/m ³ ) 0.13 0.21 0.28

Example 3-1
(Mix 7) Example 3-2
(Mix 8) Example 3-3
(Mix 9) compressive strength(MPa) 35.48 38.32 40.01 slump(mm) 225.31 250.45 266.56 entrained air content (%) 3.5 5 6 carbonation depth (mm) 25.00 25.00 25.00 total cost($NT/m ³ ) 1514.46 1684.04 1800.16 water to binder ratio 0.41 0.36 0.32 fly ash replacement ratio 0.25 0.25 0.25

4) Design of high strength fly ash mixed concrete mixture

In the above example, as a result of setting the design compressive strength of the fly ash mixed concrete composition to 30 MPa, it was confirmed that the actual compressive strength was greater than the design compressive strength, and it was confirmed that carbonation durability acts as a decisive factor in the design. In the following examples, the fly ash mixed concrete composition design was performed in such a way that the design compressive strength was 45 MPa, except that the other limiting conditions were the same. The designed composition was determined by the quality evaluation model and genetic algorithm in the same manner as in other examples, and performance evaluation was performed on fly ash mixed concrete (see Tables 10 and 11).

Example 4-1
(Mix 10) Example 4-2
(Mix 11) Example 4-3
(Mix 12) cement (kg/m ³ ) 370.43 395.22 414.55 fly ash (kg/m ³ ) 123.48 131.74 138.18 water (kg/m ³ ) 166.59 164.10 162.47 fine aggregate (kg/m ³ ) 635.39 609.73 591.24 coarse aggregate (kg/m ³ ) 953.08 914.60 886.86 superplasticizer (kg/m ³ ) 5.91 6.87 7.52 air-entraining agent (kg/m ³ ) 0.16 0.24 0.30

Example 4-1
(Mix 10) Example 4-2
(Mix 11) Example 4-3
(Mix 12) compressive strength(MPa) 45.00 45.00 45.00 slump(mm) 246.3 263.80 275.84 entrained air content (%) 3.5 5 6 carbonation depth (mm) 18.32 20.39 21.60 total cost($NT/m ³ ) 1783.16 1875.36 1945.63 water to binder ratio 0.34 0.31 0.29 fly ash replacement ratio 0.25 0.25 0.25

6 shows that the carbonization depth of the high-strength fly ash mixed concrete of the present invention is lower than the coverage depth. According to previous studies, high-strength fly ash mixed concrete has high carbonation resistance due to high carbonation content and low carbon dioxide diffusion rate (Thomas, 2013). Therefore, it is judged that compressive strength, not carbonation, acts as a decisive factor in designing a high-strength fly ash mixed concrete composition having a compressive strength of 45 MPa level.

7 shows the cost of a fly ash mixed concrete composition with various entrained air contents and strengths of the present invention. In general, it is confirmed that the concrete cost increases as the concrete strength increases in the case of a specific air mixing amount, which is supported by the results of previous studies by Lim et al., 2004 and Yeh, 2007.

5) Discussion

The present invention is summarized as follows.

The optimization design method of the air mixed fly ash mixed concrete composition of the present invention is characterized by considering the mechanical properties, workability and durability of concrete, unlike the conventional mixing design method without consideration of the durability of concrete. According to the embodiment of the present invention, carbonation durability acts as a decisive factor in the design of the air mixed fly ash mixed concrete composition having a design compressive strength of 30 MPa, which corresponds to a general compressive strength; The real compressive strength rk becomes higher than the design compressive strength; It is confirmed that the actual compressive strength and binder content should be improved when global warming is taken into account.

In the case of high-strength air-entrained fly ash mixed concrete with a design compressive strength of 45 MPa, it is confirmed that strength is a decisive factor in the design because of its high binder content and high carbonation resistance. The optimization design method of the present invention can be used to determine a threshold value of design strength through inherent durability and compressive strength control.

Addition of fly ash to the concrete mix has the advantage of reducing the total cost of concrete because the price of fly ash is lower than that of cement, whereas the strength efficiency factor of fly ash is lower than that of cement, so if the price of fly ash rises rapidly, it maintains strength. There is also a disadvantage that the total cost savings from the use of fly ash disappears because a larger amount of fly ash must be used for this purpose (Momtazia et al., 2016; Naibaho, 2018; Akhtar et al., 2019; Burciaga et al. , 2019).

The optimal design method of the air-entrained fly ash mixed concrete composition of the present invention is when using the recommended strength and entrained air of the design code to consider the evaluation model for frost damage, for example, a general predictive model for surface scaling and internal cracking. It was assumed that concrete exhibits excellent cold resistance. Through follow-up research, concrete mixtures exposed to frost will be designed, a precise evaluation model will be established for surface scaling and internal cracks, and the durability of carbonization due to frost will be thoroughly investigated.

6) Application of the present invention

It is judged that the optimal design method of the air mixed fly ash mixed concrete composition of the present invention can be practically applied in various environments. For this, the user must check the objective function, and it is judged that localization is possible by checking the information on the unit price and carbon dioxide emission of concrete components that can be secured in the country to be applied and applying it to the restricted conditions.

The user must check the limiting conditions such as mechanical properties (compressive strength), workability (slump), durability (carbonation durability and frost resistance), component range, and component ratio of the concrete to be designed, and the compressive strength, slump, and carbonation resistance Detailed equations for castability and frost resistance can be found through the design code of the present invention. Users can also use genetic algorithms to design low-cost and low-carbon dioxide concrete that meets local requirements. The specific constraint equations for compressive strength, slump, carbonation durability and frost resistance may vary from country to country, but the above genetic algorithm corresponds to a general procedure that can be used to determine global optimization results with different constraint conditions, so it is easy to apply It is considered possible

3. Conclusion

The present invention relates to an optimal design method of an air mixed fly ash mixed concrete composition in consideration of carbonation durability and frost durability. The present invention has the following characteristics.

In the present invention, it is possible to design mixed concrete in consideration of the limiting conditions of carbonation due to global warming. Through the present invention, a decisive factor was identified in the design of mixing concrete with various strengths. The present invention shows the relationship and difference between actual compressive strength and design compressive strength. The present invention provides an integrated design method in consideration of sustainability, durability, and advantages thereof.

The details of the design method proposed through the present invention are as follows.

First, the mixture optimization method consists of two parts: the objective function and the constraint condition. The objective function means the total cost including material cost and carbon dioxide emission cost. For reference, the carbon dioxide emission unit is converted into a cost unit based on the carbon price and used. The limiting conditions include compressive strength, workability, durability including carbonation durability and frost resistance, absolute volume, component range, and component ratio. In particular, carbonation models take into account global warming.

Second, the present invention uses a genetic algorithm to optimally design an air-entrained fly ash mixed concrete composition. In the present invention, a total of 12 types of examples were performed. Examples of the present invention are three examples (Example 1-1, 1-2, 1-3); Three examples (Examples 2-1, 2-2, 2-3) in the case of mild exposure (3.5%), moderate exposure (5%), and severe exposure (6%) as a mixture considering carbonation durability ; Three examples (Examples 3-1 and 3-2) in the case of mild exposure (3.5%), moderate exposure (5%), and severe exposure (6%) as a mixture considering the effect of global warming on carbonation , 3-3); High-strength concrete consists of three examples (Examples 4-1, 4-2, 4-3) corresponding to hardness exposure (3.5%), moderate exposure (5%), and severe exposure (6%). .

Third, as a result of analyzing the results of the present invention, it was confirmed that carbonation durability acts as a decisive factor in the design of the mixture of air mixed fly ash mixed concrete with a design compressive strength of 30 MPa. In the case of moderate exposure (5%), the real compressive strength was 35.76 MPa, which was found to be much higher than the design compressive strength of 30 MPa. When global warming is considered in the optimal design of the air-entrained fly ash mixed concrete composition, the actual strength and binder content should be increased, and the actual compressive strength after moderate exposure and global warming was found to be 38.32 MPa.

Fourth, in the case of high-strength concrete with a design compressive strength of 45 MPa, it was confirmed that the carbonization depth was lower than the covering depth. In addition, since the high-strength concrete has a high binder content and high carbonization resistance, it is confirmed that compressive strength acts as a decisive factor in composition design. As a result of analyzing all compositions with various air mixing amounts and actual strengths, it is confirmed that when the air mixing amount is fixed, the concrete cost increases as the concrete strength increases, and when the actual strength is fixed, the concrete cost increases according to the air mixing amount.

Fifth, the optimal design method of the air mixed fly ash mixed concrete composition of the present invention can be useful and variously applied according to the design code. Appropriate equations can be applied to the design code for mechanical properties (compressive strength), workability (slump), and durability (carbonation durability and frost resistance). However, in the genetic algorithm, a specific constraint equation may be used, but the genetic algorithm is a procedure applied in various ways and can be usefully used for overall optimization results under different constraint conditions.

The specific examples described herein are meant to represent preferred embodiments or examples of the present invention, and the scope of the present invention is not limited thereby. It will be apparent to those skilled in the art that modifications and other uses of the present invention do not depart from the scope of the invention as set forth in the claims herein.

Claims (11)

In the optimal design method of the air mixed fly ash mixed concrete composition considering carbonation and freeze-thaw,
When the computer runs the program for optimal design of air-entrained fly ash mixed concrete composition,
^{Components ( _ _ _} a component mixing range input window for inputting a lower limit and an upper limit of the component); Component ratio where lower and upper limits of the component ratio can be entered, including water/binder ratio, fly ash/binder ratio, water/solid ratio, aggregate/binder ratio, and sand ratio range input window; Compressive strength-frost-workability input window including a design compressive strength value (MPa) input window at the age of 28 days, a design slump value (mm) input window, and an air mixing amount (%) input window; Service life value (years), environmental temperature value (℃), relative humidity value (%), carbon dioxide concentration (%), cover depth value (mm), and climate change scenarios of Representative Concentration Pathways (RCP) a carbonation durability condition input window capable of inputting a carbonation durability limit condition including a type; Cement (kg/m ³ ), fly ash (kg/m ³ ), water (kg/m ³ ), fine aggregate (kg/m ³ ), coarse aggregate (kg/m ³ ), water reducing agent (kg/m ³ ), and a concrete composition content output window for outputting an optimal content of a fly ash mixed concrete composition containing an air admixture ((kg/m ³ ); a calculation execution button; and a save button; a first step of providing on the screen;
When the component mixing range input window, the component ratio range input window, the compressive strength-frost-workability input window, and the carbonation durability condition input window are all input and the calculation execution button is selected and the calculation is executed,
The program calculates the total cost as an objective function, and uses the input value to limit the compressive strength limit, workability limit, carbonation durability limit, frost durability limit, absolute volume limit, component mixing range limit Calculating the content of cement, fly ash, water, fine aggregate, and coarse aggregate, and the content of water reducing agent and air entraining agent that satisfy the conditions and component ratio constraint conditions,
The content of the cement, fly ash, water, fine aggregate, and coarse aggregate and the content of the water reducing agent and the air admixture have the minimum value of the objective function using a genetic algorithm, and the compressive strength limiting condition, workability limiting condition , carbonation durability limitation condition, frost durability limitation condition, absolute volume limitation condition, component mixing range limitation condition, and component ratio limitation condition are calculated and output to the concrete composition content output window Optimal design method of air mixed fly ash mixed concrete composition in consideration of carbonation and freeze-thaw comprising;

The method of claim 1, wherein the objective function is Equations 1 to 3:
[Equation 1]

(The above COST means the total cost of concrete; COST _M means the material cost of concrete; COST _CO2 means the cost of CO ₂ emission of concrete.)
[Equation 2]

(COST _M in Equation 2 means the material cost of concrete; m _i means the mass of cement, fly ash, water, fine aggregate, coarse aggregate, water reducing agent and air-entraining agent; Pr _i is the amount of individual components of concrete means the price.)
[Equation 3]

(COST _CO2 in Equation 3 means the cost of CO ₂ emission of concrete; Pr _CO2 means the unit price of CO ₂ (Pr _CO2 is set to NT $885.496/ton (Inc, 2019)) CO _2i is concrete refers to the CO2 emissions _of individual components of
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
The method of claim 1, wherein the compressive strength limiting condition means that the design compressive strength value at 28 days of age is greater than or equal to the actual compressive strength value at 28 days of age, and the design compressive strength value is expressed by the following Equation 4:
[Equation 4]

(f _c in Equation 4 refers to compressive strength; W refers to the mass of water; C refers to the mass of cement; FA refers to the mass of fly ash. In addition, V _air is the mixed air of (the unit of V _air is %);

is the effective water/binder ratio of concrete.)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
The method of claim 1, wherein the workability limiting condition means that the design slump value is greater than or equal to the actual slump value, and the slump value is expressed by Equation 5:
[Equation 5]

(SD in Equation 5 means the mass of sand; CA means the mass of coarse aggregate; SP means the mass of superplasticizer; C means the mass of cement and FA means the mass of fly ash.

means the water/binder ratio;

is the ratio of sand to total aggregate,

denotes the fly ash replacement ratio; 1+0.03V _air means an increase in slump due to entrained air.)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
According to claim 1, wherein the carbonation durability limiting condition means that the carbonation depth (carbonation depth) is smaller than the cover depth (cover depth), the carbonation depth is the following Equations 8 and 9:
[Equation 8]

[Equation 9]

(χ _c in Equation 8 or 9 means carbonation depth; D means carbon dioxide diffusivity of concrete; [CO ₂ ] ₀ means carbon dioxide concentration; t means exposure time; ρ _c denotes the density of cement; ρ _w denotes the density of water; RH denotes the relative humidity of exposure; α _H denotes the degree of hydration (

) means; β denotes the activation energy of carbon dioxide diffusion (β=4300); T _ref means the reference temperature (293K); T stands for environmental temperature; (V _air -2) ^* 0.01 means concrete porosity increased due to entrained air.)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
According to claim 1, wherein the frost durability limiting condition is that the damage to the concrete caused by repeated freezing and thawing is smaller than the degree of damage to the concrete of the ACI code according to the value entered in the air mixing amount (%) input window, and the compression An optimal design method of an air mixed fly ash mixed concrete composition in consideration of carbonation and freeze thawing, characterized in that it satisfies the strength limiting conditions.
According to claim 1, wherein the absolute volume limiting condition means that the sum of the volumes of the concrete components is equal to the value obtained by subtracting the air mixing amount (%) from 1m ³ , and the absolute volume limiting condition is the following Equation 10:
[Equation 10]

(m _i in Equation 10 refers to the mass of the component; ρ _i refers to the density of the component; V _air refers to the amount of air mixed (%).)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
According to claim 1, wherein the component mixing range limiting condition means that the amount of the component added is between the component mixing lower limit and the upper limit, and the component ratio limiting condition is the composition The optimal design method of an air mixed fly ash mixed concrete composition in consideration of carbonation and freeze thawing, characterized in that the mixing ratio of the elements corresponds between the lower limit and the upper limit of the ratio of the components.
According to claim 1, wherein the content of the water reducing agent is Equation 6:
[Equation 6]

(The above SP means the mass of the water reducing agent; W means the mass of water; C means the mass of cement; FA means the mass of fly ash.)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
According to claim 1, wherein the content of the air mixing agent is the following Equation 7:
[Equation 7]

(The AE means the content of the air admixture; the V _air means the air content (%); C means the mass of cement; FA means the mass of fly ash.)
: Optimal design method of air mixed fly ash mixed concrete composition considering carbonation and freeze thawing, characterized in that calculated by
A computer-readable recording medium in which the method of any one of claims 1 to 10 is recorded as a program that can be executed by a computer.

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