5.6 Phase composition of portland cement paste

     The distribution of phases in a cement paste will depend primarily on the composition of the cement clinker, the total amount of sulfate (including added gypsum), and the amount of time the cement has been hydrating.  Table 5.2 lists some phase data for a typical type I OPC paste made at a w/c of 0.45.  The oxide composition of such a cement was given in Chapter 3.  For the mature paste, it was assumed that the C3S and C2S reacted to near completion, the C3A was completely consumed, and half of the C4AF had reacted.  The phase distribution in the mature paste was estimated based on the reactions given in the previous section, assuming that the conversion of ettringite into monosulfate was complete.  In this case, the total amount of sulfate was such that some ettringite remained in the paste.  Note the low volume percent of capillary porosity in the mature paste (~11%), which is a result of the relatively low w/c of 0.45.  This indicates that the paste will be relatively impermeable, and thus resistant to many forms of degradation.  At a slightly higher w/c of 0.5, the capillary porosity would increase to about 17%, making the paste considerably more vulnerable.

Table 5.1: Phase data for a Type I OPC paste made with a w/c of 0.45.


Volume %


Density (g/cm3)

At Mixing

Mature Paste

















Gypsum (C H2)




C-S-H (solid)a




C-S-H (with gel pores)b




Portlandite (CH)




Ettringite (AFt)




Monosulfoaluminate (AFm)








Gel porosity




Capillary porosity




a Formula 1.7C-S-4H.     b Formula 1.7C-S-1.6H.

     Whereas the values in the last column of Table 5.2 were determined from a relatively complex series of calculations that took into account the specific cement composition and reactions, it is possible to estimate the overall volumes of hydration product, gel porosity, and capillary porosity for any portland cement paste using a few simple equations.  This approach and the model described below were developed by T.C. Powers, an influential cement researcher, and his coworkers in the 1940s [6],[7].  The individual hydration products are not distinguished, but are considered as a single phase with a characteristic density and internal gel porosity.  This is clearly a simplification, but it is justified on the basis of the relatively small differences in the mineral composition of ordinary portland cements.  The model also assumes that the initial and final volumes of a cement paste are equal, which is close enough to true to make no difference.
     The first step is to determine the degree of hydration of the cement, a, which varies between 0 initially and 1 for complete hydration of the cement.  The degree of hydration is proportional to the amount of water that has been chemically combined into the hydration products, which can be determined by measuring the “non-evaporable water”.  A small sample of hardened paste (not concrete) is crushed into small pieces and then dried (see Section 7.3.2) to remove the liquid  or “evaporable” water.  After weighing, the sample is ignited by heating it to 1050˚C and then weighed again.  At this temperature the hydration products decompose and the non-evaporable water is driven off, essentially returning the specimen to the original cement composition.  The degree of hydration is estimated as


where wn is the weight of non-evaporable water divided by the weight of the ignited sample.
     As a paste hydrates, the volume of hydration product (including gel porosity) increases and the volume of capillary porosity decreases.  The w/c of the paste determines the amount of space available for hydration product to form.  At higher w/c the cement can completely hydrate leaving residual capillary porosity.  At lower w/c the capillary porosity will fill up before all of the cement has reacted, stopping hydration prematurely.  Separating these conditions is a critical w/c value that provides just enough space for all of the cement to react with no leftover capillary porosity.  This value was determined experimentally by Powers and Brownyard to be w/c = 0.38 [6].  At this w/c, the fully hydrated specimen consists of only hydration product, and so the volume of hydration product is equal to the initial volume of cement and water.  Assuming that the specific volume of portland cement is 0.32 cm3/g, this gives a value of vhp=  0.70 cm3 of hydration product per gram of starting cement.  This value of vhp is independent of the w/c of the paste, and will scale linearly with the degree of hydration, giving the following general formulas:

         or                       5.9

     In the original model, the amount of gel water was defined as the amount of evaporable water in a fully hydrated specimen of w/c = 0.38, which was measured to be vgel = 0.21 g/g starting cement.  Assuming that the gel pore water has a specific volume of 1 cm3/g, this gives the formulas

         or                      5.10

     It should be noted that vacuum or oven drying a paste removes not only liquid water but also some of the water held in the structure of the C-S-H gel and aluminate phases.  Thus eq. 5.10 will give gel pore volumes that are somewhat larger than the amount of liquid water trapped inside the C-S-H gel phase.  The volume of unreacted cement in a paste is:

     or             5.11

By definition, the volume of capillary porosity is vcap = vtotvhpvcem.  Using eqs. 5.9 – 5.11 gives:

    or                   5.12

     Using a value of a = 0.95, we can compare the results of the Powers model with the calculated phase distributions for a specific cement composition shown in Table 5.2.  Using the versions of eqs. 5.9 – 5.12 on the right (normalized to paste volume) gives:

            vhp = 86.4%          vgel = 25.9%           vcem = 2.1%          vcap = 11.6%

The corresponding values from Table 5.2 are:

            vhp = 85.9%          vgel = 21.0%           vcem = 3.3%          vcap = 10.7%

     Agreement is reasonable, with the exception of the gel porosity.  In Table 5.1 the gel porosity includes only liquid water trapped in the C-S-H gel, so this is expected. 


Chemical and autogeneous shrinkage
    There are two types of volume changes that are associated with the hydration process: chemical shrinkage and autogeneous shrinkage. As the terms imply, in both cases the volume of the paste decreases. These two phenomena often occur together, and both scale with the degree of hydration, so they are frequently confused.
    Chemical shrinkage represents the change in the total saturated volume of the paste as the cement is converted to hydration products. This volume change is negative, becuase the the solid hydration products are denser than the cement and water from which they form. The main reason for this is that the effective density of water that is bound into phases such as C-S-H, CH, and ettringite is signifcantly higher than the value of 1 g/cc associated with liquid water. This may be confusing because we have previously stressed the point that the hydration products have a greater volume than the cement (only) from which they form. The difference is whether the original liquid water is included in the calculation.
    Autogeneous shrinkage occurs when the capillary pores start to empty of water in order to provide water for continued hydration. This generates capillary stresses which cause the paste to shrink. This is exacly the same mechanism that causes drying shrinkage; the only difference is where the water that leaves the capillary pores is going. Autogeneous shrinkage will only occur if there is no external supply of water to refill the capillary pores. Such a condition is called sealed curing, because in a laboratory setting it is what occurs when fresh paste is sealed into a plastic container so that no water can enter or leave. Autogeneous shrinkage will occur in pastes of any w/c subjected to sealed curing, but in practice it only becomes noticeable for w/c below about 0.5. This is because water is drained first from the largest pores, and emptying of large pores causes little capillary stress. Autogenous shrinkage will necessarily occur in the interior of large concrete or cement paste volumes, because additional water cannot be supplied from the surface. (One clever attempt to circumvent this problem is to use porous, water-saturated aggregate to provide an internal source of water, but this is impractical in most circumstances).
    In order for a cement paste to hydrate fully to = 1, there must be enough water to react all of the cement, and there must be enough space for the hydration product to form. Both of these parameters depend on the w/c of the paste, and the Powers model described above can be used to estimate the minimum w/c value for complete hydration based on each of the two criteria.

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See advanced topic: Thermodynamic Analysis of Pore Solution Concentrations
See advanced topic: Solubility Behavior of Solid Phases During Hydration

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