CC BY
12Magazine of Civil Engineering. 2019. 85(1). Pp. 123-135 Инженерно-строительный журнал. 2019. № 1(85). С. 123-135
Magazine of Civil Engineering ISSN
° 2071-0305
journal homepage: http://engstroy.spbstu.ru/
DOI: 10.18720/MCE.85.10
Modified water-cement ratio rule for the design of air-entrained concrete
L.I. Dvorkin,
National University of Water Environmental Engineering, Rivne, Ukraine E-mail: dvorkin. leonid@gmail. com
Keywords: Modified C/W; the volume of air entrained; cement consumption; strength and frost resistance of concrete; pore volume of aggregate; composition of lightweight concrete.
Abstract. Designing concrete compositions, containing entrained air, is usually done by means of empirical proportioning, which is quite a laborious and lengthy process. In the article design formulae are experimentally justified with rule of modified C/W, which is complex due to known empirical dependencies, and allow us to find the content of concrete components with desired strength, frost resistance, and density properties. Conducted experimental studies are: compression method for determining the volume of entrained air as well as standard methods for determining the strength and frost resistance of concrete. Lastly, generated formula was verified on an example for calculating the compositions of heavy concrete with a given strength and frost resistance and structural claydite-concrete with desired strength and density.
1. Introduction
One of the fundamental fields in concrete science is methodology of concrete compositions design, aimed at achieving concrete with a set of desired properties.
D. Abrams has for the first time proposed two approaches [1] for concrete compositions design: a so-called 'trial method' or experimental proportioning and a «preliminary calculations method» and considered that both approaches should be based on a water-cement ratio rule (low). Practice has confirmed this condition proved by Abrams however many subsequent researches have shown [2-5] that Abrams's statement that concrete strength for given materials and their processing conditions is defined just by the ratio between the water and cement volumes, used for manufacturing the concrete mixture' is some exaggeration and the word 'just' should be replaced by 'mainly' or 'basically'. In addition to the water-cement - W/C (or cement-water - C/W) ratio and cement strength or its activity (Rcem), in calculating the concrete composition it is necessary to take into account additional factors affecting the properties of concrete.
In 1920, having processed more than 50000 tests, Abrams proposed an empirical formula:
f =— (1)
J cm .X ' v '
A
where k and A are coefficients;
X is the water to cement volume ratio for cement with a density of 1500 kg/m3.
Many studies were carried out to specify the water-cement ratio rule and increase the number of factors, considered in equations for predicting concrete strength [6-12]. The most important investigations in this field
Dvorkin, L.I. Modified water-cement ratio rule for the design of air-entrained concrete. Magazine of Civil Engineering. 2019. 85(1). Pp. 123-135. DOI: 10.18720/MCE.85.10.
Дворкин Л.И. Модифицированное правило водоцементного соотношения для проектирования бетонов, содержащих воздух // Инженерно -строительный журнал. 2019. № 1(85). С. 123-135. DOI: 10.18720/MCE.85.10
This open access article is licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
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are based on structural approach. In these studies the initial preconditions are based on hypotheses of interrelation of concrete strength and its structure, though these hypotheses are essentially different.
There is a number of design equations for concrete strength, trying to consider the complex interaction mechanism between aggregates and cement matrix at heterogeneous material's collapse [1, 6, 13]. These equations represent a big interest to studying possibilities of predicting concrete strength variation due to changes in strength and deformation characteristics of phases composing the material. However, at present time using these equations for concrete compositions design is usually inconvenient or impossible.
An attempt to increase the number of factors, considered in concrete compositions design and to consider the influence of aggregates features resulted in the «real» W/C theory [6] (W/C)r:
(W / C)r = W - W°SC, (2)
where W and C are total content of water and cement; Ws and Wcr.s are water demand of fine and coarse aggregates; S and Cr.S are mass content of fine and coarse aggregates respectively.
Water demand parameters of fine and coarse aggregates characterize the water quantity that should be added to cement paste per unit of its mass in order to obtain a corresponding mortar mixture with C:S (cement:sand) = 1:2 composition or a concrete mixture with C:S:Cr.S (cement:sand:crushed stone) = 1:2:3.5 composition, having the same slump after mixing as cement paste with normal consistency [6].
In opinion of some researchers [6], "real" W/C characterizes the cement paste in concrete after immobilization of water by the aggregates through a certain structure formation period. In our opinion «real» W/C can be interpreted as W/C of cement paste in concrete mixture at the moment of equal moisture carrying potentials.
Using the (W/C)r concept for concrete with constant entire W/C value enabled to estimate the dependence of concrete strength on some factors that affect redistribution of water between the cement paste and aggregates. At the same time the algorithm of using (W/C)r in the concrete design is complex and requires additional assumptions.
Great opportunities to take into account various factors affecting the properties of concrete when design the its composition open experimental models obtained using statistical methods for the processing of experimental data [14-24]. However these models are usually local and fair under the specified conditions of the experiments.
Presently for predicting concrete strength and for concrete composition design the following typical formula is widely used [1]:
fcm = ¿Kern C / W - b), (3)
where fcm is the concrete strength at 28 days;
C and Ware the masses of cement and water per 1 m3 of the concrete mix;
A and b are empiric coefficients, depending on the initial materials features and structural type of concrete; Rcem is the compressive cement strength at 28 days.
Still Bolomey has mentioned that linear formula for prediction concrete strength fcm = k(C /W - 0.5)
is valid just if C/W = 0.9...2.5 [1]. For wider diapason a nonlinear version of the formula was proposed. The
general nonlinear function fcm = f (C / W) is often replaced in practice with linear piecewise dependences,
proposed and proved by B. Skramtaev and Y. Bazhenov [1]. Alongside with Eq. (3) a number of other formulas, based on a water-cement rule are known (Table 1). They, however, are almost not applied because a relatively more complex structure and necessity of additional data. Another reason for limited use of these formulas is lack of essential increase in prediction accuracy.
It is more convenient to consider the factors, along with C/W, which significantly affect the strength of concrete, the system of amendments SAi for the coefficient A in formula (3). Such a system was developed by V. Sizov [1].
A number of computational and experimental dependencies [12, 24-27] were proposed to take into account the characteristics of aggregates and additives in the designation of concrete compositions.
Table 1. Main design formulas for predicting concrete strength, used for concrete compositions design [1].
Authors Relation for strength prediction Notations
R. Feret N. Belyaev American Concrete Institute Manual of Concrete Practice [8] B.Skramtaev, Y.Bazhenov M. Simonov L.Kaiser, R.Chehova I.Rybiev fcm = k (y + F ] «> V cem w air J R f = cem (5) Jcm A(W / C)3/2 ( * fcm = 117.07e"OT/C (6) fcm = ARcem (C / W - 0.5) for W/ C > 0.4, fcm = ARcem (C/ W + 0.5) for W/ C < 0.4 L„ = °-49 ARcem ( 3^ C ^ ) (8) f =(2.3 Rcem +100) C/W - 80 Jcm 10 ^ ' R* f = (10) Jcm , .n K ' W / C I (W / C )* J Vcem - absolute cement volume, Vw - water volume, Vair - volume of air voids in concrete, k - coefficient, depending on materials quality, used for concrete, manufacturing and curing conditions, Rcem - ultimate cement strength W / C = 0.41 - 0.82 A - coefficient, depending on aggregates quality. (W/C)* - water-cement ratio of maximum possible cement stone strength, R* - maximum possible cement stone strength, n - coefficient, depending on features of concrete macrostructure and applied aggregates.
I.Ahverdov V.Shmigalsky KR f = cem (11) m 1 + 1 65K 0.95 K nc (W / C) 1.65Knc n.c f = R 0.6 - 0.0014W Jcm cem , x1/3 (l2) (W / C) Kn.c - normal consistency of cement paste.
To take into account the influence of mineral additives and the entrained air on the strength of concrete, it was suggested [1] to use the modified Bolomey formula:
fcm = Kb
C + KceAd W + V,,
-0.5 I (13)
where fcm is the compressive strength, Kb is the constant of Bolomey, C is mass of cement, Ad is the mass of mineral additive, W is the mass of used water,
Vair is the volume occupied by the entrained air equivalent the mass of water,
Kc.e. is the coefficient of «cementing efficiency» or «cement equivalent» of 1 kg additive.
The formula (14) reflects a depending that can be considered the "rule of modified W/C" (or C/W). In accordance with this rule the strength of concrete additionally to the effect of the ratio of cement and water content by weight can be affected the ratio of equivalent amounts of active mineral additives and entrained air. The ratio of the total content of these components of concrete uniquely determines the strength of concrete.
Based on this rule, a number of studies of concrete compositions design with fly ash and other mineral additives were performed [1, 7, 25, 28, 29]. At the same time for concrete, containing entrained air, this rule, insufficiently experimentally substantiated.
The purpose of the research, the results of which are given in the article, was to determine the possibility the applicability of the calculated dependencies of concrete strength based on the modified C/W for design of concrete compositions take into account the volume of air entrained by the addition of the surface-active substances (SAS) and porous aggregates.
As an air-entraining additive was used air-entraining resin (neutralized Vinsol) - a product of neutralization of the wood resin by caustic soda after extraction of turpentine from it. The additive introduced into concrete mixtures in an amount of 0.01...0.03 % by weight of cement, previously dissolved in water at t = 30...40 °C. The volume of entrained air in concrete mixtures was determined by compression method based on the law Boyle-Marriott, establishing the relationship between the volume of air and the applied pressure at a constant temperature (EN 206-1).
For the manufacture of concrete mixtures used Portland cement CEM II/ A-S with the mineralogical composition of clinker, %: C3S - 57.10; C2S - 21.27; C3A - 6.87; C4AF - 12.9. Specific surface of cement -340 m2/kg. The compressive strength of cement corresponded to the class of 42.5 N (EN 197-1). Fine aggregate of concrete served the quartz sand with a modulus of fineness Mk = 1.95 and a content of dust and clay impurities of 2.1 %. As a coarse aggregate of the normal weight concrete, granite crushed stone of fraction 5...20 mm was used, light concrete - claydite gravel of fraction 5...20 mm with bulk density of 500...800 kg/m3.
Testing the strength of concrete was carried out on control samples-cubes with a fin length of 100 mm in accordance with GOST 10180-2012 (EN 12390-3:2009).
The frost resistance of concrete was determined by the ultrasonic method (Russian State standard GOST 26134-2016). The tests are carried out until the "ultrasound-velocity-number of cycles" line will break, after that the reduction in ultrasound velocity will have higher intensify.
Experimental researches were carried out in the research laboratory of the building materials tests of the National University of Water Environmental Engineering (Ukraine, Rovno).
Concrete with entrained air. When calculating the compositions of concrete with entrained air, the formula (13) with Ad = 0 can be brought to mind:
were A is coefficient taking into account the quality of raw materials [1];
Rcem is compressive strength of cement, MPa;
C and W is cement and water consumption in concrete mix by weight, kg/m3;
Vair is the volume of entrained air Vair, l/m3.
An analysis of the effect of the volume of entrained air on formula (15) on the strength of concrete for various values of C/W and W is shown in Figure1.
On average, the calculated decrease in concrete strength for each percentage of air involved is 3.5...4.5 %. A tendency to a decrease in the relative effect of entrained air on strength is observed at C/W = const with an increase in water consumption in concrete. The calculated data are close to experimental (Figure 1).
The main purpose of air-entraining additives in concrete is to increase its frost resistance by creating a system of uniformly distributed closed air pores. This fact has been convincingly proved by the practice of construction and numerous studies. Processing our experimental data [1] included results of concrete frost resistance measurements in freezing cycles at -15...-20 °C and thawing at +15...±5 °C until strength decreases no
more than 5 % for a rather wide compositions diapason (/c2m8 = 15...40 MPa, W = 140...220 l/m3, Vair = 0.8...6.5 %). The data are approximised by a formula that has the following type:
2. Methods
3. Experimental results and discussion
(14)
F = fA2 exp
(15)
fcm, MPa 80 -|—
20 -I-1-1-1-1-1-1-
0 1 2 3 4 5 6 7 Vair, %
Figure 1. Influence of the volume of entrained on the concrete compressive strength
1 - C/W = 1.5; W = 200 l/m3. 2 - C/W = 1.5; W = 160 l/m3. 3 - C/W = 2; W = 200 l/m3.
4 - C/W = 2; W = 160 l/m3. 5 - C/W = 2.5; W = 200 l/m3. 6 - C/W = 2.5; W = 160 l/m3
(A = 0.6; Rcem = 50 MPa) Experimental results: x - W = 200 l/m3; • - W = 160 l/m3.
For the investigated concrete A3 = 0.35, Ai and A2 are varied depending on the water demand and correspondingly mixtures workability (Table 2).
As it follows from analyzing Eq. (15), at entrained air content of 3...5 % the concrete frost resistance increases by 3.6 times (Figure 2). For concrete strength above 30.40 MPa the relative increase of critical number of freezing-thawing cycles, achieved by entraining air a little increases. It can be explained by higher influence of closed pores of contraction origin.
Table 2. Values of coefficients Ai and A2 in Eq. (16) for concrete mixtures with various workability.
Concrete mixtures workability Ai A2
Plastic concrete mixtures (Slump Sl = 9.12 cm) 0.34 1.68
Low-plastic concrete mixtures (Slump Sl = 1.4 cm) 0.91 1.47
Non-plastic concrete mixtures 2.48 1.25
As the empirical data on the values of parameters Ai and A2 is accumulated, Eq. (15) can be widely used either for predicting frost resistance or for concrete compositions design.
The required entrained air volume in % can be found according to a formula, obtained from Eq. (15):
' F
ln
A fA
V = y Ucm y (16)
ar 0.35 ■ V '
At the same time when designing concrete compositions with an air-entraining additive at given values of its strength and frost resistance, along with a significant increase in the latter the necessity of certain overestimating of the given concrete strength, depending on the entrained air volume, should be considered (Figure 3). The overall positive effect of reducing the consumption of cement can be quite significant, especially in concrete with high values of frost resistance and a moderate normalized value of strength. From Figure 4, in particular, it follows that fcm = 20 MPa and F200 are provided without the addition of entrained air at W/C = 0.5 (C/W = 2) with the introduction of entrained air - W/C = 0.62 (C/W = 1.61).
Using the formula (14) at the design stage of concrete compositions and having previously determined the water consumption by reference or laboratory data, it is possible to calculate C/W, Vair and C values to
ensure the specified indicators of concrete strength and frost resistance. The consumptions of aggregates and their ratio are using known recommendations [1-6].
Figure 2. Affect of entrained air on concrete frost resistance (for concrete mixtures with Slump Sl = 1...4 cm) : 1 - f^8 = 70 MPa; 2 - = 50 MPa; 3 - f^8 = 35 MPa; 4 - f^ = 20 MPa .
fcm,
MPa 55 50 45 40 35 30 25 20
X I "
2 ■■
- -i--
F,
cycles 600
500 400
0 1 2 3 Vaii, %
Figure 3. Dependence between the entrained air volume, concrete strength (fcm) (1)
and frost resistance (F) (2). Note: concrete strength is calculated using a formula (14), concrete frost resistance (15).
fcm,
MPa 40 -I
35 -30 -25 20
0.3
0.62. 0.72
T—n-rr
-100
1.1 W/C
Figure 4. Relationship between W/C and given values of concrete strength (Rc)
and frost resistance (F). 1 - fcm without entrained air; 2 - fcm with 20 l of entrained air; 3 - F without entrained air; 4 - F with 20 l of entrained air.
Example 1
Calculate the required values of the cement-water ratio (C/W), the volume of entrained air (Vair) and
28
cement consumption to produce concrete with compressive strength at 28 days fcm = 30MPa and frost resistance F = 300 cycles. Apply Portland cement with compressive strength of 50 MPa, ordinary aggregates. Slump of the concrete mix - Sl = 1.4 cm.
1. According to the formula (16) we find the required volume of entrained air. The values of the coefficients Ai and A2 will be determined by the Table 2.
lnl 300
^ = y e^30"8 J = = 3.05 % (30.5 l/m3 ).
2. Using the formula (14), taking the value of the coefficient A = 0.6 and the water consumption of 200 l/m3 will determine the required value of C and C/W:
fcm = 0.6 -50
^ - 0.5 1;
W + Var
C (fcm + 05 ARc )(W + Vair ) (30 + 05 • °.6 • 5°)(200 + 30 5) 34575W3
C ARC 0.6 • 50 345./5Kg/m,
C / W = C: W = 345.75:200 = 1.73.
Lightweight Concrete. As known, for lightweight concrete on porous aggregates the water-cement ratio rule in its traditional formulation is unacceptable, as strength of such concrete is determined not just by cement stone density and accordingly strength, but also by strength and volumetric concentration of porous aggregates. Many formulas were suggested for calculating lightweight concrete strength [7]. Part of them characterized linear relation between concrete strength and cement consumption or C/W, considering the influence of mechanical and structural features of aggregates by generalized coefficients. Other formulas directly considered physic-mechanical parameters of porous aggregates, but were only indirectly related with composition parameters. These formulas require complicated calculations and provide approximate results.
Existing empirical formulas are of interest, mainly, for comparing materials based on various types of porous aggregates, but have low potential for concrete composition design. The existing practice of lightweight concrete composition design is based usually on using average tabulated data with subsequent experimental validation for given initial materials.
An integral parameter that takes into account both C/W and, indirectly, through pore volume of the aggregate, its strength, can be the parameter Z:
V
Z =--cm--(17)
V + (P -Wb )V +V ■ '
w \ ag ab.ags ag air
were Vcem, Vw, Vag, Vair are volumes of cement, water, aggregates and air, l/m3; Pag is aggregate porosity, Wab.ag is aggregate water absorption.
Claydite concrete compositions with compressive strength (fcm) of 10...30 MPa at 28-days, density (pc) of 1500...1800 kg/m3 were calculated using recommendations given in [33] for claydite gravel with bulk
density (pbd) 600...800 kg/m3 and water absorption (Wab.ci) 0.18.0.22. Quartz sand was used as fine aggregate. The obtained results, presented in Table 3 and Figure 5, enable to approximate the dependence Rc = f Z) by a linear equation:
fcm = ARcZ, (18)
where A = 1.7.
Experiments have confirmed the formula and accordingly the assumed physical preconditions (Table 4). The average strength deviation between experimental results and those calculated according Eq. (18) was 6 %.
Инженерно-строительный журнал, № 1(85), 2019
Table 3. Calculation results for parameter Z and strength of claydite concrete.
No. Pc, kg/m3 pCI , kg/m3 W kg/m3 V*cl, l/m3 Kil C, kg/m3 Z fcm, MPa C/W
Claydite porosity Pel = 0.4
1 1500 800 197 507 0.22 230 0.257 17.50 1.17
2 1800 800 197 344 0.22 205 0.255 17.37 1.04
3 1500 800 197 507 0.22 320 0.358 24.35 1.62
4 1800 800 197 344 0.22 270 0.336 22.87 1.37
5 1600 800 197 468 0.22 380 0.436 29.64 1.93
6 1800 800 197 344 0.22 340 0.424 28.80 1.73
7 1600 800 197 468 0.22 450 0.516 35.10 2.28
8 1800 800 197 344 0.22 400 0.498 33.89 2.03
Pel = 0.55
9 1500 600 207 437 0.22 240 0.220 14.99 1.16
10 1800 600 207 274 0.22 210 0.228 15.49 1.01
11 1500 800 197 507 0.22 320 0.283 19.27 1.62
12 1800 500 212 252 0.18 300 0.317 21.56 1.42
13 1500 700 202 472 0.19 420 0.364 24.77 2.08
14 1800 600 207 274 0.22 360 0.390 26.55 1.74
15 1600 600 207 388 0.22 480 0.462 31.43 2.32
16 1800 700 202 300 0.19 420 0.437 29.72 2.08
Pel = 0.7
17 1500 800 197 507 0.22 230 0.168 11.46 1.17
18 1800 600 207 274 0.22 210 0.200 13.61 1.01
19 1500 600 207 437 0.22 340 0.263 17.90 1.64
20 1800 600 207 274 0.22 290 0.276 18.79 1.40
21 1500 800 197 507 0.22 400 0.293 19.93 2.03
22 1800 800 197 344 0.22 340 0.303 20.60 1.73
23 1500 800 197 507 0.22 470 0.344 23.41 2.39
24 1800 700 202 300 0.19 420 0.382 25.95 2.08
V*cl - volume of claydite gravel.
Table 4. Experimental and calculated values of claydite concrete strength.
No. Calculated concrete strength, MPa Concrete density, kg/m3 Materials consumptions, kg/m3 Volume of entrained air, % Z Experimental concrete strength, MPa
cement claydite sand
1 15 1500 224 767 800 479 3.2 0.222 15.1
2 15 1600 243 440 600 882 2.8 0.222 14.9
3 20 1500 369 380 500 691 2.7 0.296 19.8
4 20 1600 289 708 800 563 2.3 0.296 19.8
5 30 1600 477 572 700 477 2.1 0.445 29.4
6 30 1800 392 520 800 835 1.8 0.445 30.1
Notes: 1. Denominator shows the bulk density of claydite (Cl). 2. Slump for all compositions was 5 cm, 28-day strength of cement was 40 MPa.
From equations (18) and (19) it can be found that when is used for lightweight concrete, dense sand without air-entraining additives cement consumption:
xr _ fcm (Vw + (Pag Wab.ag )Vag + Vair .. m Vcem --TZ-' (19)
AKH
C - VcemPcem , (20)
were pcem - density of cement (pcem ~ 3.1).
Figure 5. Dependence of claydite concrete strength (fcm) on C/W and parameter Z: 1 - claydite porosity is 0.4; 2 - 0.55; 3 - 0.7.
Using parameter Z in formula for lightweight concrete strength enables to propose rather simple its composition design method.
Example 2
Determine the consumption of cement to obtain claydite concrete with a strength 25 MPa and a density of 1700 kg/m3 on claydite gravel with a bulk density of pbcl = 700 kg/m3 and quartz sand. The slump of the mixture Sl = 5 cm. The strength of cement Rcem = 50 MPa. Intergranular hollowness of claydite P0cl = 0.44. Claydite porosity Pci = 53 %, water absorption Wab.ci = 20 %, Vair = 15 l/m3.
1. Determine the desired "modified C/W (parameter Z) to ensure the specified strength of concrete from the formula (17):
Z=tt5T0=0294
2. Determine the required water content to achieve the desired workability of the concrete mixture according to the empirical formula [1, 6]:
W = 2.33SI - 0.04pcl + 230;
W = 2.33 • 5 - 0.04 • 700 + 230 = 214 l/m3.
3. Calculate the volume concentration of p and the volume content of Vci the claydite gravel in concrete, using the formula:
cp = 1 - P>, Va= 1000(,
were a - coefficient of moving apart of coarse aggregate grains by cement-sand mortar (according to reference data [1] for concrete with a density of pc = 1700 and a bulk density of claydite pbcl = 700, a = 1.45).
( = 1 - 0.44 • 1.45 = 0.362.
Craydite consumption:
Vcl = 1000 • 0.362 = 362 l/m3.
4. Cement consumption is found by the formulas (19), (20)
Vcem = 0.294 • (214 + (0.53 - 0.2)• 362) +15 = 113 l/m3;
C = 113 • 3.1 = 350.3 kg/m3.
HH®eHepH0-CTp0HTe^bHhiH ^ypHaa, №2 1(85), 2019
4. Conclusions
1. Modifying C/W taking into account of the influence of entrained air allows to correct of the strength of concrete calculated dependence that can be used for design concrete compositions with normalized values of concrete compressive strength under compression and frost resistance.
For light concrete, modifying C/W is advisable in view of the air volume contained in the pores of the porous aggregate. Using the proposed parameter Z, it is possible to calculate the composition of light weight concretes, taking into account the influence of both the cement-water ratio and the porosity of the aggregates.
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16. Hwang, K., Noguchi, T., Tomosava, F. Prediction model of compressive strength of fly-ash concrete. Cement Concrete Res., 34, 2004. Pp. 2269-2276. [Online]. URL: ftp://ftp.ecn.purdue.edu/olek/PTanikela/To%20Prof.%20Olek/Data/Strength%20Activity%20In dex/INFORMATION/strength%20as%20a%20function%20of%20blaines.pdf
17. Hamid-Zaden, N., Jamili, A., Nariman-Zadeh, A., Akbar-Zadeh. A polynomial model for concrete compressive strength prediction using GMDH - type neural networks and genetic algorithem. Proceedings of the 5th International Conference of System Science, Canary Islands, Spain, 2006. Pp. 16-18. [Online]. URL: https://www.researchgate.net/publication/254457742_A_Polynomial_Mo del_for_Concrete_Compressive_Strength_Prediction_using_GMDH-type_Neural_Networks_and_Genetic_Algorithm
18. Zain, M., Abd, S. Multiple regression model for compressive strength prediction of high performance concrete. J. Applied Sci. 2009. No. 9. Pp. 155-160. DOI: 10.3923/jas.2009.155.160
19. Saadoon, T., Gomes-Meijide B., Garcia A. New predictive methodology for the apparent activation energy and strength of conventional and rapid hardening concretes. Cement and Concrete Research. January 2019. Vol. 115. Pp. 264-273. DOI: 10.1016/j.cemconres.2018.10.020.
20. DeRousseau, M., Kaspzyk, J., Srubar, W. Computational design optimization of concrete mixtures: A revier Cement and Concrete Reseach. Vol. 109. 2018. Pp. 42-53. [Online]. URL: https://doi.org/10.1016/j.cemconres.2018.04.007
21. Mayercsik, N., Vandamme, M., Kurtis, K. Asessing the efficiency of entrained air voids for freeze-thaw durability through modeling. Cement and Concrete research. 2016. Vol. 88. Pp. 43-59. DOI: 10.1016/j.cemconres.2016.06.004.
22. Jiao, D., Shi, C., Yuan, Q., An, X., Liu, Yu. Mixture design of concrete using simplex centroid design method. Cement and Concrete Composites. 2018. Vol. 89. Pp. 76-88. DOI: 10.17632/xhss7xv6wz.1.
23. Dvorkin, L., Zhitkovsky, V., Stepasiuk, Y. A method for design of high strength concrete composition considering curing temperature and duration. Construction and Building Materials. 2018. Vol. 186. Pp. 731-739. DOI: 10.1016/j.conbuildmat.2018.08.014.
24. Larsen, O.A., Narut, V.V. Samouplotnyayushchiysya beton s karbonatnym napolnitelem dlya obyektov transportnoy infrastruktury [Self-compacting concrete with limestone powder for transport infrastructure]. Inzhenerno-stroitelnyy zhurnal. 2016. № 8(68). S. 7685. DOI: 10.5862/MCE.68.8. (rus)
25. Dvorkin, L., Zhitkovsky V., Ribakov Y. Concrete and mortar production using stone siftings, 2018, CRC Press, Roca Raton, London, New York. 155 p.
26. Furmanov, N.Ye. Blagopriyatnyy sostav betona dlya izgotovleniya vodonepronitsayemykh konstruktsiy po sisteme «Belaya vanna» [The favorable composition of concrete for the manufacture of waterproof structures using the «White Bath» system]. Inzhenerno-stroitelnyy zhurnal. 2009. № 3 (5). C. 11-16. [Online]. URL: http://engstroy.spbstu.ru/index_2009_03/furmanov_gidroizoliaciya.pdf (rus)
27. Barabanshchikov, Yu.G., Belyayeva, S.V., Arkhipov, I.Ye., Antonova, M.V, Shkolnikova, A.A, Lebedeva, K.S. Vliyaniye superplastifikatorov na svoystva betonnoy smesi [Influence of superplasticizers on the concrete mix properties]. Inzhenerno-stroitelnyy zhurnal. 2017. № 6(74). S. 140-146. DOI: 10.18720/MCE.74.11. (rus)
28. Hedegaord, S., Hansen, T. Modified water/cement ratio law for compressive strength of fly ash concretes. Materials and Structure. 1992. Vol. 25. Pp. 273-283. DOI: 10.1007/BF02472668.
29. Abdulahi, M., Ojeade G. Modified water-cement ratio law for compressive strength of rice husk ash concrete. Nigerian Journal of Technology. 2017. Vol. 36. No. 2. Pp. 373-379. DOI:10.4314/njt.v36i2.8.
Contacts:
Leonid Dvorkin, +38(068)3533338; dvorkin.leonid@gmail.com
© Dvorkin, L.I., 2019
Инженерно-строительный журнал, № 1(85), 2019
Инженерно-строительный журнал
сайт журнала: http://engstroy.spbstu.ru/
ISSN
2071-0305
DOI: 10.18720/MCE.85.10
Модифицированное правило водоцементного соотношения для проектирования бетонов, содержащих воздух
Л.И. Дворкин,
Национальный университет водного хозяйства и природопользования, г. Ровно, Украина E-mail: dvorkin. leonid@gmail. com
Ключевые слова: Модифицированное Ц/В; объем вовлеченного воздуха; расход цемента; прочность и морозостойкость бетона; объем пор заполнителя; состав легких бетонов.
Аннотация. Проектирование составов бетона, содержащего вовлеченный воздух, обычно выполняется с помощью эмпирических подборов, что является довольно трудоемким и длительным процессом. В статье экспериментально обоснованы расчетные формулы с помощью правила модифицированного Ц/В, которое основано на известных эмпирических зависимостях и позволяет находить содержание компонентов бетона с заданными параметрами прочности, морозостойкости и плотности. Приведены результаты экспериментальных исследований, выполненных с помощью компрессионного метода определения объема вовлеченного воздуха, а также стандартных методов определения прочности и морозостойкости бетона. Полученные формулы проверены на примерах расчета составов тяжелого бетона с заданной прочностью и морозостойкостью и конструкционного керамзитобетона с заданными значениями прочности и плотности.
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Литература
14. Dvorkin L., Dvorkin O., Ribakov Y. Mathematical experiments planning in concrete technology. Nova Science Publishers, New York, 2012. 173 p. [Электронный ресурс]. URL: https://www.researchgate.net/publication/293205467_Mathematical_experiments_planni ng_in_concrete_technology
15. Kheder G., Gabhan A., Suhad Mathematical model for the prediction of cement compressive strength of the ages of 7 and 28 days // Mater. Struct. 2003. No. 36. Pp. 693-701. DOI: 10.1007/BF02479504.
16. Hwang K., Noguchi T. and Tomosava F. Prediction model of compressive strength of fly-ash concrete // Cement Concrete Res. 2004. No. 34, Pp. 2269-2276. [Электронный ресурс]. URL: ftp://ftp.ecn.purdue.edu/olek/PTanikela/To%20Prof.%200lek/Data/Stre ngth%20Activity%20Index/INF0RMATI0N/strength%20as%20a%20function%20of%20blaines.pdf
17. Hamid-Zaden N., Jamili A., Narim-Zadeh A., Akbar-Zadeh. A polynomial model for concrete compressive strength prediction using GMDH - type neural networks and genetic algorithem. Proceedings of the 5th International Conference of System Science, Canary Islands, Spain, 2006. Pp. 16-18. [Электронный ресурс]. URL: https://www.researchgate.net/publication/254457742_A_Polynom ial_Model_for_Concrete_Compressive_Strength_Prediction_using_GMDH-type_Neural_Networks_and_Genetic_Algorithm
18. Zain M., Abd S. Multiple regression model for compressive strength prediction of high performance concrete // J. Applied Sci. 2009. No. 9. Pp. 155-160. DOI: 10.3923/jas.2009.155.160.
19. Saadoon T., Gomes-Meijide B., Garcia A. New predictive methodology for the apparent activation energy and strength of conventional and rapid hardening concretes // Cement and Concrete Research. January 2019. Vol. 115. Pp. 264-273. DOI: 10.1016/j.cemconres.2018.10.020.
20. DeRousseau M., Kaspzyk J., Srubar W. Computational design optimization of concrete mixtures: A revier // Cement and Concrete Reseach. Vol. 109. 2018. Pp. 42-53 [Электронный ресурс]. URL: https://doi.org/10.1016/j.cemconres.2018.04.007
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22. Jiao D., Shi C., Yuan Q., An X., Liu Yu. Mixture design of concrete using simplex centroid design method // Cement and Concrete Composites. 2018. Vol. 89. Pp. 76-88. DOI: 10.17632/xhss7xv6wz.1.
23. Dvorkin L., Zhitkovsky V., Stepasiuk Y. A method for design of high strength concrete composition considering curing temperature and duration // Construction and Building Materials. 2018. Vol. 186. Pp. 731-739. DOI: 10.1016/j.conbuildmat.2018.08.014.
24. Ларсен О.А., Наруть В.В. Самоуплотняющийся бетон с карбонатным наполнителем для объектов транспортной инфраструктуры // Инженерно-строительный журнал. 2016. № 8(68). С. 76-85. DOI: 10.5862/MCE.68.8.
25. Dvorkin L., Zhitkovsky V., Ribakov Y. Concrete and mortar production using stone siftings, 2018, CRC Press, Roca Raton, London, New York, 155 p.
26. Фурманов Н.Е. Благоприятный состав бетона для изготовления водонепроницаемых конструкций по системе «Белая ванна» // Инженерно-строительный журнал. 2009. № 3 (5). C. 11-16 [Электронный ресурс]. URL: http://engstroy.spb stu.ru/index_2009_03/furmanov_gidroizoliaciya.pdf
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28. Hedegaord S., Hansen T. Modified water/cement ratio law for compressive strength of fly ash concretes // Materials and Structure. 1992. Vol 25. Pp. 273-283. DOI: 10.1007/BF02472668.
29. Abdulahi M., Ojeade G. Modified water-cement ratio law for compressive strength of rice husk ash concrete // Nigerian Journal of Technology. 2017. Vol. 36, No. 2. Pp. 373-379. DOI: 10.4314/njt.v36i2.8.
Контактные данные:
Леонид Иосифович Дворкин, +38(068)3533338; эл. почта: dvorkin.leonid@gmail.com
© Dvorkin, L.I., 2019
