The work of Powers and Brownyard revisited: Part 1 - Jos Brouwers

1704H.J.H. Brouwers / Cement and Concrete Research 34 (2004) 1697–1716For the cements listed in Table 1, the fit of w g /c has beencomputed using Eqs. (32) and (37), and the computedvalues are included in Table 1 as well.The fitted and measured values are in good agreement,but the agreement is less good than between the measuredand fitted values of w n /c (Table 1). The constancy of w g /w nfor a given cement is not a trivial result and supports theviewpoint (previous section) that the fractional rate ofhydration of the clinker phases is approximately the same.Each clinker phase produces hydration products with theirown retention of gel water; it can be concluded that allphases hydrate more or less congruently.In Table 1, w d /c is also included, both measured andcomputed, following from Eqs. (3) and (36) asw d =c ¼ð1 þ BVÞw n =c ¼ Bw n =c:ð38ÞComparing w d /c and w n /c (the difference is w g /c), onecan conclude that the amount of gel water is almost equal tothe amount of nonevaporable water (BV c 1).The amount of retained water per clinker phase can beobtained by substituting x C3 s =1 (c = m C3 s), x C2 s =1 (c =m C2 s), etc. into Eqs. (32) and (36)–(38), yielding:w d ¼ 0:359 m C3 S; w d ¼ 0:360 m C2 S; w d ¼ 1:508 m C3 A;w d ¼ 1:016 m C4 AF;ð39Þrespectively. This result can be written in moles ofwater per mole of clinker phase using Eq. (34)n H;d ¼ 4:55 n C3 S; n H;d ¼ 3:44 n C2 S; n H;d ¼ 22:6 n C3 A;Fig. 2. w g /V m vs. relative humidity for the cement samples used in heat ofadsorption measurements (Fig. 4-2, taken from p. 554, Ref. [1]).n H;d ¼ 14:2 n C4 AF:ð40ÞAs said, Powers and Brownyard [1] have expressed thegel water in the nonevaporable water. It enables the couplingclosely follows the degree of hydration indeed. In view ofthis direct relation, Powers and Brownyard [1] introducedand measured the property V m /w n , which was referred toas k, accordingly:w g =w n ¼ BV¼ 4k ¼ 4V m =w n :ð36ÞIn Table 1, the measured w g /c for the listed cements areincluded (obtained by multiplying the measured 4V m /w nand w n /c). These values are taken from Ref. [1] (Tables 2–6,pp. 596–600).Furthermore, it was recognised that the amount ofinternal surface (i.e., the amount and type of hydrationproducts) depends on the composition of the cement.Powers and Brownyard [1] therefore recommended thefollowing empirical fit:V m =w n ¼ 0:230 x C3 S þ 0:320 x C2 S þ 0:317 x C3 Aþ 0:368 x C4 AF:ð37ÞFig. 3. Empirical relationship between total evaporable water per unit V mand original water –cement ratio for samples cured 180 days or longer(Fig. 3.13, taken from p. 502, Ref.[1]).