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

H.J.H. Brouwers / Cement and Concrete Research 34 (2004) 1697–1716 1699‘‘compressed water’’. The mass of compressed water thuscomprises:w d ¼ w n þ w g :ð3ÞThe specific volume of all compressed water followsfromm d ¼ w nm n þ w g m gw n þ w g¼ w nm n þ w g m gw d; ð4Þwhereby Eq. (3) has been inserted. The specific volume ofall water follows fromm t ¼ w cm w þ w n m n þ w g m gw c þ w n þ w g¼ w cm w þ w d m dw c þ w d; ð5Þin which the capillary water mass, w c , has been introduced.The sum of capillary water and gel water is also referred toas evaporable water:w e ¼ w c þ w g :The volume of the unreacted (or anhydrous) cement isð6ÞV c ¼ðc 0 cÞm c ¼ð1 mÞc 0 m c : ð7ÞIn which the concept of maturity is introduced, defined asc ¼ mc 0 ;ð8Þnowadays more usually called ‘‘hydration degree’’. It is anoverall property, although the plain clinker phases may havedifferent reaction rates. Joined in cement, these mineralsreact, however, more congruently, and for hydration degreesabove 50%, this overall hydration degree serves well todefine the degree of reaction of each clinker phase [19,20].Powers and Brownyard [1] referred to the total solidphase either as ‘‘V s ’’, which follows from adding V hc and V c(yielding c 0 m c + w n m n )oras‘‘V b ’’, which also includes the gelwater space, i.e., comprising V hp + V c (=c 0 m c + w n m n + w g m g =c 0 m c + w d m d ; see Fig. 1).The volume of the pore water follows fromV w ¼ðw 0 w d Þm w ¼ðw 0 w n w g Þm w : ð9ÞThe total volume of the water and cement becomesV t ¼ c 0 m c þ w 0 m w :So that as volume shrinkage of the system isV s ¼ V t V hp V c V w ¼ w n ðm w m n Þþw g ðm w m g Þð10Þ¼ w d ðm w m d Þ: ð11ÞThe total capillary pore volume follows from adding Eqs.(9) and (11):Under dry conditions, V s will be filled with air and /orvacuum, and hence, the total water in the system followsfromw t ¼ w 0 ;ð13Þthat is, the total water equals the initial mixing water. In apaste that hardens under saturated conditions, this volumewill be filled with external water; in that case V w becomesequal to V cp , and the total water mass of the system willincrease by imbibition and follows from Eq. (11) as:w t ¼ w 0 þ V s¼ w 0 þ w dðm w m d Þ: ð14Þm w m wThe total water in the system is also related to the initialcement content of the system, and Eq. (14) is then dividedby c 0 :w t¼ w 0þ m w dc 0 c 0 cw d m dm w c; ð15Þwhereby Eq. (8) has been inserted. From this equation, onecan see that the total mass of the paste increases withincreasing degree of hydration when external water mayenter the paste.Note that the imbibed water is accounted for by thesecond term on the right-hand side of Eq. (15), and thatthis water increases the amount of capillary water, w c .Furthermore, one can derive the maximum achievablematurity as:m Vw tc 0w d; ð16Þcwith m = 1 in case the right hand-side exceeds unity. UsingEqs. (13) and (14), the maximum maturity follows fromm Vw 0c 0w dcand m Vw 0c 0w d m d; ð17Þm w cfor sealed and saturated hydration, respectively. From Eq.(17) and considering that m d < m w , it follows that theamount of initial water can be smaller than the waterneeded for complete hydration, w d , owing to the inflow ofexternal water by shrinkage. Physically, this implies that toachieve complete hydration (m = 1), upon mixing, lesswater is required than w d /c, as the paste will imbibe themissing water by the internal volume that is created byshrinkage (imbibed water mass). The mass of imbibedwater is related to the mass of cement and is:V cp ¼ V w þ V s ¼ w 0 m w w n m n w g m g¼ w 0 m w w d m d : ð12ÞV sm w c ¼ w dcw d m dm w c :ð18Þ