Accounting for the Influence of HeatMoisture Treatment Mode When Designing Concrete Composition
Leonid Dvorkin ^{†,*}, Vadim Zhitkovsky ^{†}, Ruslan Makarenko ^{†}

National University of Water and Environmental Engineering, Rivne, Ukraine

† These authors contributed equally to this work.
* Correspondence: Leonid Dvorkin
Academic Editor: Mostafa Seifan
Special Issue: New Trends on Construction Technologies and Sustainable Building Materials
Received: January 12, 2023  Accepted: February 20, 2023  Published: February 24, 2023
Recent Progress in Materials 2023, Volume 5, Issue 1, doi:10.21926/rpm.2301009
Recommended citation: Dvorkin L, Zhitkovsky V, Makarenko R. Accounting for the Influence of HeatMoisture Treatment Mode When Designing Concrete Composition. Recent Progress in Materials 2023; 5(1): 009; doi:10.21926/rpm.2301009.
© 2023 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.
Abstract
The article proposes a method that considers the parameters of heat and moisture treatment of concrete when designing its composition. Based on the analysis of experimental data, formulas are proposed that allow taking into account the type and characteristics of cement, the characteristics of aggregates, the effect of temperature and duration of steaming, and the watercement ratio. Graphs and nomograms have been obtained, which makes it possible to simplify the calculation procedure according to the proposed method. Typical numerical examples of the application of this technique are given.
Keywords
Concrete; steaming; watercement ratio; strength; design
1. Introduction
In concrete composition designing, experimental and calculationexperimental methods are used [1,2,3]. The calculationexperimental method involves a preliminary determination of the concrete composition using basic calculated dependencies, followed by adjustment of these compositions in laboratory batches. Compared with the experimental method, this method significantly reduces labor costs and time for determining concrete composition with specified normalized parameters in specific production conditions.
For normalweight concrete produced under normal temperature conditions, the basic design dependencies are the dependences of the concrete strength on the watercement (W/C) or cementwater (C/W) ratio, based on Feret, Abrams, Powers, Bolomey and modified by other researchers [3]. Calculating the required cementwater ratio for steamed concrete becomes much more complicated, especially in achieving the required concrete strength immediately after steaming. As shown by practical experience and many studies [3,4,5,6,7,8,9,10,11,12,13], the strength of concrete after steaming is significantly affected by its mode parameters. It affects both the value of the cement strength realized in concrete and the required C/W to achieve a given strength.
In [14], after studying the concrete strength of 40 batches of cement of various types, strength classes and chemicalmineralogical composition, an strength equation was proposed depending on the cement strength and C/W. At the same time, the concrete strength and the Portland cement used in it were considered after steaming in one mode (2 + 3 + 6 + 2 (hours) at 80°C (for Portland slag cement 90°C)). An analysis of the formula proposed in this paper [14] shows that at C/W <3, a linear dependence for compressive strength is practically maintained. For C/W >3, it is proposed to introduce an average correction for the nonlinearity of this dependence.
An actual task in the steamed concrete compositions design is to consider the kinetics of its hardening after heat treatment. Known dependencies [11], based on the logarithmic law of concrete strength increase in time, as applied to steamed concrete, require clarification.
Summarizing the state of the problem of developing design dependencies necessary for the implementation of the calculationexperimental method for designing compositions of steamed concretes, we can state that it requires additional research. This article presents the results of a study aimed at developing the parameters of the concrete composition, considering the mode parameters of heat and moisture treatment and other technological factors.
2. Materials and Methods
The studies were carried out by analyzing the data in the works [11,13,14] and approximating these data using empirical equations. To confirm the equations obtained, an experiment was carried out, which consisted in studying the effect of steaming parameters (holding time before steaming, temperature and duration of isothermal heating) on the strength characteristics of standard cementsand samples (according to EN 1961 [15]) and normal weight concrete (according to EN 123901 [16]).
Portland cement and slag cement were used in the research. The cement is made based on typical medium aluminate clinker (tricalcium aluminate С_{3}А = 6.2–7.1%, tricalcium silicate С_{3}S = 58.5–61.3%) and additionally included: Portland cement  5% of gypsum, Slag Portland cement  5% of gypsum and 50% of blast furnace slag. The following characteristics were determined: compressive strength 4 hours after steaming, compressive strength 28 days after steaming, and strength under normal conditions at different ages. The steaming of cement and concrete was carried out in a laboratory steaming chamber according to the following regime: holding until steaming  2 hours, raising the temperature  3 hours, isothermal holding ($\tau_{is}$)  varied from 2 to 18 hours, cooling  2 hours (2 + 3 + $\tau_{is}$ + 2). The steaming temperature varied from 60 to 95°С.
Concrete samples (cubes 100 × 100 × 100 mm) were made using mediumgrained sand and crushed granite stone 5…20 mm. The concrete C/W was changed in the range from 1.55 to 3.
3. Results and Discussion
In the practice of calculating C/W when designing the concrete composition [11], the following formula is widely used:
\[ \operatorname{R}_\text{cmp}=\operatorname{AR}_\text{cem}(\operatorname{C}/\text{W}\operatorname{b}), \tag{1} \]
where R_{cmp} is concrete compressive strength; R_{cem} is the 28day cement strength, obtained by testing of the standard cementsand mortar samples; A and b are an empirical coefficients.
An increase in the resolution of the equation (1) is achieved using the multiplicative coefficient pA_{i}:
\[ \text{p}\text{A}_\mathrm{i}=\text{A}\cdot \text{A}_\mathrm{i}\ldots \text{A}_\mathrm{n}, \tag{2} \]
where А is the coefficient that depends on the quality of aggregates; А_{i} are a coefficient, considering additional influence of ith factor (i = 1…n) on concrete strength [12]. The influence of various factors on coefficient А was widely investigated [11,12].
The coefficient A = pA_{i} assumes that all factors A_{i} are independent. Considering that the calculated strength values are only basic and are subject to experimental correction, this assumption can be accepted with a known accuracy range.
The usual technological information allows considering multiplicative coefficient, in addition to the main coefficient A, up to 2, 3 or more coefficients A_{i}.
The influence of the normal hardening duration can be approximately described by the wellknown logarithmic dependence [2]:
\[ \text{A}_\tau=\text{lg}n/\text{lg}28=0.69\text{l}\text{g}n, \tag{3} \]
where n is the hardening duration in days.
The concrete strength calculation, subjected to heat treatment, has several features.The concrete strength calculation, subjected to heat treatment, has several features. Analysis of various experimental studies shows that the steamed concrete strength depends on the heat treatment parameters, the strength of cement during heat treatment and C/W.
The coefficients А_{i} can be concretized by statistical processing of experimental data for a certain industrial enterprise. Table 1 presents an example of coefficients, characterizing effects on concrete compressive strength of: initial materials quality (А), hardening duration ($\text{A}_\tau$), thermal treatment ($\text{A}_{\tau,\text{t}}$), antifreezing and hardening accelerating admixtures (А_{ac}), as well as calculated (R_{cmp,c}) and real (R_{cmp,r}) concrete strength values at C/W = 1.4 for Portland cement with the strength of 40 MPa.
Table 1 Values of coefficients А_{i}, calculated (R_{cmp.c}) and real (R_{cmp.r}) concrete strength values (R_{cem} = 40 МPa, C/W = 1.4)
Deviations of calculated strength values from average real ones have not exceeded 17%. The strength of steamed cement (${R}_{{cem}}^{{st}}$) can be expressed as:
\[ \text{R}_{\text{cem}}^{\text{st}}=\text{R}_{\text{cem}}\text{K}_{\text{e}}, \tag{4} \]
where K_{e} is efficiency coefficient, characterizing the influence of the different technological factors on strength of the standard cement – sand specimens at W/C = 0.4 after heattreatment.
The K_{e} value varies from 0.55 to 0.75, depending on the features cement used.
Below are given graphs and corresponding regression equations (Figure 1) of the main efficiency coefficient $\text{K}_\text{e}^0$ depending on the isothermal heating duration $\tau_{is}$ and temperature t_{t.t }for Portland cement and Portland Slag cement with the strength after steaming of 50 MPa ($\text{K}^0_{e_{p.c}}$) and 40 MPa ($\text{K}^0_{e_{s.p.c}}$) (respectively), obtained by the experimental data [13] processing.
Figure 1 Graphs for determining coefficients $\text{K}^0_\text{e}$: a  using Portland cement; b  using Portland Slag cement; ◊  t_{t.t} = 60°C; □ t_{t.t} = 80°C; ○  t_{t.t} = 95°C.
The value of $\text{K}^0_\text{e}$ was found from the condition that $\text{K}^0_\text{e} = \text{R}_{\text{cem}}^{\text{st}}/\text{R}_{\text{cem}}$. Approximating the experimental data (Table 2) the following equations were obtained:
\[ \rm{K}_{e_{\text{p.c}}}^{0}=(0.38770.0032t_{\text{t.t}})\ln\tau_{\text{is}}+0.012t_{\text{t.t}}0.5096, \tag{5} \]
\[ \mathrm K^0_{{\text{e}_\text{s.p.c}}}=(0.36930.0016\mathrm t_{\text{t.t}})\ln\tau_{\text{is}}+0.0098\mathrm t_{\text{t.t}}0.565. \tag{6} \]
Table 2 Calculated and experimental values of $\text{K}^0_\text{e}$ and relative strength values.
Table 3 shows the experimental and calculated values of $\text{K}^0_\text{e}$ obtained by Eq. (9, 10), as well as experimental values of $\text{K}^0_\text{e}$ obtained by Kayser [14] and the relative concrete strength $\text{R}_\text{c}^\text{st}/\text{R}_\text{c}^{28}$ at W/C = 0.4 following [13,14]. $\text{R}_\text{c}^\text{st}$ is the compressive strength of steamed concrete, МPa; $\text{R}_\text{c}^{28}$ is the compressive strength of concrete hardened at 20°С at 28 days). An analysis of the calculated and experimental values of $\text{K}^0_\text{e}$ shows their high convergence (the average deviation of the $\text{K}^0_\text{e}$ values, calculated by Eq. (9, 10) from the experimental data is 5%).
Table 3 Calculated values of $\text{R}_\text{c}^\text{st}$, МPa.
The essential factors, affecting K_{e}, are the chemicalmineralogical composition, the mineral admixtures content and the cement strength:
\[ \text{K}_\text{e}=\text{K}_\text{A} \text{K}_\text{D} \text{K}_{\text{R}_\text{cem}}\text{K}^0_\text{e}, \tag{7} \]
where $\text{K}^0_\text{e}$ is the main efficiency coefficient value that can be found from the Eq. (5, 6); K_{А}, K_{D}, K_{Rcem} are correcting coefficients, depending on the aluminate content in cement, the mineral admixtures content and the steamed cement strength at 28 days.
Taking into account the data given in [14], for high aluminate cement at $\tau_{is}$ ≤ 3 h K_{А} = 0.9; $\tau_{is}$ ≥ 6 h; K_{А} = 0.8 for low aluminate cement at $\tau_{is}$ ≤ 3 h K_{А} = 0.8; $\tau_{is}$ ≥ 6 h K_{А} = 0.95; $\tau_{is}$ ≥ 9 h; K_{А }= 1–1.1.
The K_{D} coefficient value depends on the mineral admixtures’ type and content. With content of the mineral admixtures is up to 10%, the strength of cement during steaming is usually constant. With a content of mineral admixtures of 20% a certain reduction of $\text{R}_\text{cem}^\text{st}$ is observed with shortened steamcuring cycles. At $\tau_{is}$ ≤ 4 h adding 20% of blast furnace slag and fly ash to cement cause an average strength decrease of 10% (K_{D} = 0.9), pozzolana admixtures  15% (K_{D} = 0.85) [17]. At $\tau_{is}$ > 4 h  K_{D} = 1.0.
For cement with 28day strength of 50 MPa K_{Rcem }= 1 [18], 40 MPa K_{Rcem} = 1.05; 30 MPa K_{Rcem} = 1.15; 55 MPa K_{Rcem} = 0.95.
The steamed concrete strength at 28 days may be higher or lower than that of normally hardened concrete [13]. Researches and practical experience, show that with an optimal steamcuring cycle, strength loss can be minimized or eliminated as early as 28 days.
To obtain the C/W, providing the steamed concrete strength after 28 days, it is convenient to use the general equation for the concrete strength:
\[ \mathrm{R}_{\mathrm{cmp}}=\mathrm{pA}_\mathrm{i} \ \cdot \ \mathrm{R}_{\mathrm{cem}}(\mathrm{C}/\text{W}0.5). \tag{8} \]
According to the results of experimental data processing [13,14], the coefficient (А_{1}) for steamed concrete with compressive strength $\text{R}_\text{cmp}^\text{28}$ up to 30 МPa equals 0.85–0.95, for $\text{R}_\text{cmp}^\text{28}$ > 30 МPa it is from 0.95 to 1.05. The lower values of А_{1} are characteristic of shortened heat treatment cycles and concrete mixtures with high water demand. The value of the coefficient А_{2} can be taken according to the wellknown recommendations [13].
Kayser and Chekhova [14] investigated concrete strength variation after steaming. Based on the obtained experimental data the following equation was proposed:
\[ \mathrm{R}_\mathrm{c}^{\mathrm{st}}=0.41(\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}+9)\mathrm{C}/\text{W}0.83(\mathrm{C}/\text{W})^20.35\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}7, \tag{9} \]
where $\mathrm{R}_\mathrm{c}^{\mathrm{st}}$ is the concrete strength (MPa) 4 hours after the steaming cycle (2 + 3 + 6 + 2 at 80°С (for Slag Portland cement 90°С) using cement with strength of $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$ (МPa), after steaming according to the same cycle.
Analysis of the experimental data [3] and Eq. (9), carried out by the authors, shows that for C/W ≤3 the linear dependence $\text{R}_\text{c}^{\text{st}}=\text{f(C/W)}$ is strictly enough complied (Table 3). Just at C/W >3, which is rather seldom in practice, an average correction for the nonlinearity of Eq. (9) can be applied:
\[ \Delta \text{R}_\text{c}^{28}=5(\text{C/W}3)\quad\text{} \tag{10} \]
According to our data, for composition design it is rational to express the steamed concrete strength $\mathrm{R}_\mathrm{c}^{\mathrm{st}}$ as well as $\text{R}_\text{c}^\text{28}$ using Bolomey formula:
\[ \mathrm{R}_\text{c}^{\mathrm{st}}=\mathrm{pKR}_{\mathrm{wtm}}^{\mathrm{st}}(\mathrm{C}/\text{W}\mathrm{b}), \tag{11} \]
where pK = KK_{1}K_{2}K_{3}…K_{n} is a multiplicative coefficient, considering the influence of various factors on steamed concrete strength (K is the basic coefficient, characterizing the effect of $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$; K_{1} – coefficient, depending on concrete mixture workability; K_{2} – coefficient, taking into account the effect of steamed concrete aggregates features; K_{3} – coefficient, considering strength growth due to hardening accelerators addition).
Using Eq. (11) for approximating the data, calculated according to Eq. (9), is acceptable (see Table 3). The values of basic coefficient K vary depending on $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$ within the interval between 0.5 and 0.67. By applying average values of the coefficient K = 0.66 for $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$ = 2025 МPa and K = 0.53 for $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$ = 3040 МPa the deviation in the values of $\mathrm{R}^{\mathrm{st}}_{\mathrm{cem}}$ calculated according to Eqs. (9) and (11) were below 10%.
Coefficient b in Eq. (11) varies insignificantly for the entire range of $\mathrm{R}_\mathrm{c}^{\mathrm{st}}$ values (Table 3) and can be assumed to be equal to 0.74. Coefficient K decreases as the steamed cement strength increases (Table 3), which shows that the influence of the last on concrete strength has a certain nonlinearity. This conclusion also follows from Eq. (13).
The coefficient K, given in Table 3, are valid for lowslump concrete mixtures, based on crushed stone and mediumgrained sand. Steamed concrete strength at C/W = const is significantly affected by water content and correspondingly workability, which can be taken into account in Eq. (15) by coefficient K_{1}. For concrete with slump Sl = 1  4 сm the value of K_{1} = 1, and for those with Sl ≥ 9 сm  K_{1} = 0.9, if Vebe time Vb = 30–50 sec then K_{1} = 1.1 (Table 4).
Table 4 Experimental and calculated values of concrete strength after steaming.
The influence of the steamed concrete aggregate characteristics affects both through a change in water content and directly through a change in C/W, which is necessary to achieve the desired strength. In the last case a coefficient K_{2} is added to Eq. (15). For regular aggregates K_{2} = 1. However it can be assumed that K_{2} = 0.95 if crushed stone or gravel has reduced strength as well as if the content of weak grains of clay, silt and dust content is rather high; K_{2} = 0.9 for sand with fineness modulus below 1.5.
An essential reserve of necessary C/W reduction of steamed concrete can be provided by strong growth due to hardening accelerators, considered by coefficient K_{3} in Eq. (11), and further hardening after thermal treatment.
The steamed concrete strength considering further hardening up to 1 day can be found in Eq. (12):
\[ \mathrm{R}_{\mathrm{c}_{_1}}^{\mathrm{st}} \ = \ \mathrm{R}_\mathrm{c}^{\mathrm{st}}+\mathrm{K}_\mathrm{t}\text{I}lg\left(\tau_{\mathrm{p}.\mathrm{p}}/\tau_{\mathrm{p}.\mathrm{p}}^{\mathrm{0}}\right)\mathrm{R}_\mathrm{c}^{28}, \tag{12} \]
where І is the concrete hardening intensity after the heat treatment; $\mathrm{\tau}_{\mathrm{p.p}}$  post steaming period (0.5–24 h.); $\mathrm{\tau}_{\mathrm{p.p}}{}^0$ = 4 h.; K_{t}  temperature coefficient (at an average temperature of concrete post steaming period 20°С – K_{t} = 1.0; 30 – 40°С – K_{t} = 1.1 – 1.2; 10°С – K_{t} = 0.8, for concrete based on Slag Portland cement K_{t} = 0.7); $\text{R}_\text{c}^{28}$ is the 28day strength of normal hardening concrete.
Equation (13) for calculating / at $\mathrm{\tau}_{\mathrm{p.p}}$ ≤ 1 day, was obtained by the authors processing the experimental data [13]:
\[ \rm{I}=(0.000634R_c^{28}0.03254)\tau_{\text{is}}0.01R_c^{28}+0.5787, \tag{13} \]
where $\tau_{is}$ is the isothermic heating duration, h.
For calculations according to Eq. (12), it is possible to use the nomogram presented in Figure 2.
Figure 2 Nomogram for calculating the increase in relative concrete strength $\Delta \text{R}_\text{c} = \mathrm{K_tI}lg $ $\left(\tau_\text{p.p}/\tau_\text{p.p}^0\right)$ after steaming and poststeaming period up to 1 day.
$ \text{A}_\text{t}{}^{\mathrm{\tau}_ {p.p}}$ = 1  28 days the intensity of concrete strength growth is practically independent of steaming mode parameters. Concrete strength at this hardening interval can be found according to the following formula:
\[ \mathrm{R}_{\mathrm{c}_{_2}}^{\mathrm{st}}=\mathrm{R}_{\mathrm{c}_{_1}}^{\mathrm{st}}+\mathrm{K}_{\mathrm{t}}\dfrac{\mathrm{R}_{\mathrm{c}}^{28}\mathrm{R}_{\mathrm{c}_{_1}}^{\mathrm{st}}}{{l}g\mathrm{28}}{l}g\mathrm{\tau}_{\mathrm{p.p}}. \tag{14} \]
The proposed quantitative dependences enable the calculation of C/W for steamed concrete with given strength parameters at different temperatures and duration of hardening, taking into account the initial materials’ properties and considering hardening after steaming (Table 5). It also allows quantitative estimation of different technological solutions to reduce cement consumption and heat energy.
Table 5 Examples of calculating C/W and concrete thermal treatmentparameters.
Calculating C/W for steamed concrete is expedient when it is complicated to obtain it experimentally or express composition design is necessary. For the wide application of this technique, it is desirable to accumulate experimental data obtained with various raw materials and heat treatment parameters.
4. Conclusions
 The equations of 28 days and the tempering strength of steamed concrete are experimentally substantiated, allowing us to determine the required values of C/W, taking into account the steaming mode and the main technological factors.
 To find the strength of cement developed under a given steaming regime, it is proposed to find the efficiency factor depending on the temperature and duration of isothermal heating of concrete.
 Calculated dependencies are given, which make it possible to establish an increase in the strength of steamed concrete during subsequent hardening.
 The obtained quantitative dependencies and recommendations make it possible to find the values of the required cementwater ratio for concrete that can be steamed under given conditions. The cementwater ratio is the initial indicator for calculating concerete composition.
Author Contributions
Conceptualization, V.Z. and L.D.; methodology, V.Z. and R.M.; software, V.Z. and R.M.; validation, V.Z. and R.M.; formal analysis, V.Z. and L.D.; investigation, V.Z.; resources, L.D.; data curation, V.Z.; writing—original draft preparation, V.Z. and L.D.; writing—review and editing, R.M.; visualization, V.Z.; supervision, L.D.; project administration, R.M.; funding acquisition, R.M.
Competing Interests
The authors have declared that no competing interests exist.
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