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

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1710H.J.H. Brouwers / Cement and Concrete Research 34 (2004) 1697–1716volumes of the right-hand sides of Eqs. (53) and (54),deducted with the volumes by the CH, and taking accountthat part of the water is compressed to 12.97 cm 3 /mol(nonevaporable water) and the gel water part to0.9 18.02 cm 3 /mol = 16.22 cm 3 /mol (x H,g ).The H/S values for saturated C-S-H found here are lowerthan the H/S ratio put forward by Young and Hansen [13].These authors studied the reaction of pure and fully hydratedC 3 S and proposed C/S = 1.7 and H/S = 4 for the C-S-H thusformed. This water content was based on dynamic shrinkage–weightloss curves of thin specimens of C 3 S paste;whereby the time allowed for hydration was not specified.From Lu et al. [37], it follows that the H/S ratio decreaseswith hydration time: H/S = 4.56 (3 days), 3.93 (28 days) and3.60 (60 days). The H/S value after 126–479 days of curingderived here, namely, H/S = 3.2, is compatible with thistrend. In other words, water- saturated C-S-H binds an excessof water at early ages (supersaturation), which is released.Based on the aforementioned high H/S, Young andHansen [13] found by extrapolation that the density of C-S-H should range from 1.85 to 1.90 g/cm 3 in the saturatedstate. The authors compared this with the saturated geldensity of 1.76 g/cm 3 ‘‘as computed by Powers [10]’’. ButPowers [10] actually mentions that the ‘‘dry weight ofcement gel’’ (i.e., dried hydration product) attains a valueof 0.567 cm 3 /g ( = 1.76 g/cm 3 ), hence, not referring to thesaturated gel (hydration product) but, rather, to the dried gel,i.e., q hp (P-dried).On the other hand, the H/S ratio for saturated C-S-Hfound here are in accord with the values found by Fujii andKondo [38,39] and Taylor [40]. Based on synthesized C-S-H gels from a solution, the former authors found thecomposition C x SH x + 0.8 and, later, C x SH x + 0.92 . The authorsconsidered C-S-H to be a solid solution of CH and a calciumsilicate hydrate. Based on an experimental analysis ofmature cement pastes, Taylor [40] derived a similar formulationfor saturated C-S-H: C x SH x + 1.7 . Substituting x = 1.7into these formulations yields compositions that are close toC 1.7 SH 3.2 found here.Based on the previous section and in the foregoingdiscussion on the hydration of alite and belite, here, it isconcluded that for cement (and C-S-H), the density ofsaturated hydration product q hp (saturated) is typically2.25 g/cm 3 .To facilitate the modeling of cement hydration reactions,it is desirable to define a composition, molar volume anddensity of (mature) P-dried and saturated C-S-H that can beused for the C 3 S and C 2 S reactions. On the basis of thepresent results, a representative overall formulation of P-dried C-S-H would comprise C 1.7 SH 1.2 , with a density of2.86 g/cm 3 (Table 2). This density is based on the specificmolar volumes that follow from the present analysis of theC 3 S and C 2 S reactions, whereby the difference in nonevaporablewater content is accounted for by using 12.97cm 3 /mol as the effective molar volume of the combinedwater. On the basis of the values listed in Table 4b, in thecase of compressed gel water (x H,g = 16.22 cm 3 /mol), itfollows that C 1.7 SH 3.2 (M C-S-H = 213.1 g/mol) and x C-S-H =94.6 cm 3 /mol (i.e., q C-S-H =2.25 g/cm 3 and U C-S-H = 34%) provides the best results. The proposed compositionsof the C-S-H and its properties are included in Table 2.This molar volume is based on the specific molar volumesof C-S-H that follow from the present analysis of the C 3 Sand C 2 S reactions (Table 4b), whereby the difference in gelwater content is accounted for by using 16.22 cm 3 /mol asmolar volume of this water.For the computation of the molar volume of saturated C-S-H that has higher water content (e.g., young paste), fromthe previous section, it follows that the additional water(layers) will not be compressed and should be assigned aspecific molar volume of 18.02 cm 3 /mol (as most likelyonly the first two water layers are compressed). Hence, thedensity and porosity can be expressed as followsq C1:7 SH 3:2þy¼U C1:7 SH 3:2þy¼213:09 þ 18:02y94:60 þ 18:02yhgicm 3 ; ð56Þ32:44 þ 18:02y94:60 þ 18:02y ; ð57Þrespectively, with y z 0. For y = 0, Eqs. (56) and (57) yieldthe values included in Table 2. When y = 0.8 is substituted,q C-S-H = 2.0 g/cm 3 , Which comes closer to the valuesreported in [13], namely 1.85–1.90 g/cm 3 , as discussedabove. From Lu et al. [37], it follows that the H/S ratiodecreases with hydration time: H/S = 4.56 (3 days), 3.93 (28days) and 3.60 (60 days), implying y = 1.36 (3 days), 0.73(28 days) and 0.40 (60 days) if the paste is supersaturated,while from this study, it follows that y = 0 for saturatedmature paste (aged for half a year or so and longer). Afunction of the form H/S = 3.2 + y = 3.2 + g 1 exp( g 2 t) isfitted through the data of Lu et al. [37], yielding g 1 = 4.60and g 2 = 2.23 10 2 day 1 .InFig. 5, the data and fitare depicted.4.3. Properties C-S-HFig. 5. Experimental data by Lu et al. [37] and fits.
H.J.H. Brouwers / Cement and Concrete Research 34 (2004) 1697–1716 1711When the relative humidity drops below 100%,2 V y < 0 applies. The value of y versus the relativehumidity is assessed with the cement gel isotherm (Fig. 2)given by Powers and Brownyard [1] and assuming that thisisotherm is applicable to pure C-S-H, being the mostabundant reaction product. The said gel isotherm relatesw g /V m to the relative humidity, and at relative humidities ofapproximately 0% (P-dried) and 100%, indeed, w g /V mamounts to 0 and 4, respectively (see Section 3), whichwill correspond to 0 ( y = 2) and 2 ( y = 0) mol of gel waterretained, respectively. For relative humidities of 11%, 40%and 80%, w g /V m amounts to 0.8, 1.5 and 2.5, respectively,corresponding to C 1.7 SH 1.6 ( y = 1.6), C 1.7 SH 2 ( y = 1.2)and C 1.7 SH 2.5 ( y = 0.7), respectively. The composition at11% RH is in accord with the values reported by Taylor [2],and the water content is lower (again) than found by Youngand Hansen [13] (C 1.7 SH 2.1 ). This difference might becaused by the age of their paste, as discussed in theforegoing. For 2 V y < 0, the gel space is not completelyfilled with water anymore. Based on this concept, the gelspace still amounts 2 16.22 cm 3 /mol ( = 32.44 cm 3 /mol)per mole of C-S-H, for all RHs. For all relative humidities,the porosity thus follows from Eq. (57), with y = 0 substituted,being the previously mentioned 34%.In the range 2 V y V 0, the gel space is not completelyfilled with water anymore, while the total volume of the C-S-H remains constant. The density in this range therefore readsq C1:7 SH 3:2þy¼213:09 þ 18:02y94:60hgicm 3; ð58ÞIn the foregoing, some physical properties of C-S-H havebeen specified for C/S = 1.7, (super-)saturated at differentages and unsaturated (when the RH drops below 100%).Based on the information from the present study, it is alsopossible to assess the properties for C/S p 1.7.As first step, the composition in the P-dried state isconsidered. As discussed before, in this section, Kantro etal. [35] and Taylor [40] found formulations of the typeC x SH x + y , applicable to 1 V x V 2, whereby y amounts to0.5 and 0.25, respectively. Lu et al. [37] found x = 1.2and y = 0.70 after 60 days. Accordingly, the formulationC x SH x 0.5 seems appropriate to P-dried C-S-H, implyingthat C and H are reduced to the same extent. This iscompatible with Fujii and Kondo [38,39], who modelled C-S-H as a solid solution of CH and a calcium silicate hydrate.Accordingly, a change in the C/S ratio (x) of the C-S-H ismodelled by a change in CH content; using the molar massesand volumes of C 1.7 SH 1.2 and CH (Table 2), the followingexpression is put forward for P-dried C-S-H in case C/S p 1.7:177:05 þ 74:10ðx 1:7Þhgiq Cx SH x 0:5¼62 þ 33:05ðx 1:7Þ cm 351:08 þ 74:10xhgi¼5:82 þ 33:05x cm 3 ; ð59ÞThe next step is to determine the composition andphysical properties of saturated C-S-H. From the literature,one cannot conclude unambiguously the amount of evaporablewater for C/S p 1.7. Accordingly, two concepts arediscussed.Case 1: constant gel waterFujii and Kondo [38,39] and Taylor [40] found formulationsof the type C x SH x + y for saturated C-S-H, likewisefor P-dried C-S-H, whereby now, y = 0.8–1.7. Taylor [40]gives y = 1.7 for saturated C-S-H and y = 0.25 for P-driedC-S-H, implying that an extra 1.95 mol of water are retainedwhen 1 mol of P-dried C-S-H is saturated, regardless of thevalue of x. For x = 1.7, this H/S value of 1.95 is compatiblewith the H/S value of 2 found here. Based on the foregoingliterature, a change in the C/S ratio (x) of the C-S-H ismodelled by a change in CH content, whereas the amount ofgel water remains unchanged. Using the molar masses andvolumes of C 1.7 SH 3.2 and CH (Table 2), the followingexpression is put forward for saturated C-S-H, C/S p 1.7and 2 V y < 0 as:213:09 þ 74:10ðx 1:7Þþ18:02yhgiq Cx SH xþ1:5þy¼94:60 þ 33:05ðx 1:7Þ cm 387:12 þ 74:10x þ 18:02yhgi¼38:42 þ 33:05x cm 3 ; ð60ÞSee also Eq. (58), which holds for mature paste. For2 V y < 0, the gel space is not completely filled with wateranymore, but its volume is not affected.Based on the present C-S-H model, the gel spaceamounts to 2 16.22 cm 3 /mol ( = 32.44 cm 3 /mol) per moleof C-S-H, for all C/S and for 2 V y < 0 (all RH); therefore,the porosity follows asU Cx SH xþ1:5¼32:4494:60 þ 33:05ðx 1:7Þ ; ð61ÞAccording to this equation, the gel porosity increases withsmaller C/S (x) as the gel water remains 2 mol of water/molof C-S-H, whereas the P-dried mass decreases.As said, the present C-S-H model is based on the conceptof 2 H/S gel water for all C/S ratios at RH = 100%. Todetermine y versus other RH, one could use the informationprovided by the gel isotherm for C/S = 1.7, again,yielding the general expressions C x SH x 0.1 ( y = 1.6),C x SH x + 0.3 ( y = 1.2) and C x SH x + 0.8 ( y = 0.7) for RHof 11%, 40% and 80%, respectively, applicable to all C/S.Case 2: variable gel waterLu et al. [37] found that the amount of gel water islower when C/S drops from 1.7 to 1.2. In addition, for C/S = 1.2, they measured a decreasing H/S ratio with hydrationtime: H/S = 3.89 (3 days), 2.07 (28 days) and 1.66 (60
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