Volume of hydration produts
The total space available to occupy by productsof hydration is the summation of absolute volume of fresh cement and the volume of mixing water. Of these, if small loss of water under the contraction of the cement paste and that due to bleeding is ignored, the water consumed by chemical reaction with C2S and C3S was found to be 21 and 24 percent (very roughly) of the mass of two respective silicates.
If the final reaction of hydrate C4AF is
The respective figures of C3AF and C3A are 37 and 40 percent. Equation (1) is also vary approximately due to our inadequate knowledge of stoichiometry of the hydration products and cannot be ascertained the amount of chemically combined water.
Figure-1: Gel formation in cement paste (Paul Bennison)
a) Cement paste just after mixing
b) Initial stiffening-starting
reaction after mixing
c) Initial hardening-formation
of physical structure
d) Later gradual
hardening-infilling pores with gel
The average value of specific gravity of hydration product in saturated structure, inclusive of pores available in the possible densest structure, is 2.16.
Here we are providing a demonstration of calculation of volume change during hydration.
Mass of cement=100 g
Specific gravity of cement=3.15
That is absolute volume of hydrated cement=100/3.15=31.8 ml
Volume of non-evaporable water= 23ml (23% of mass of cement)
Volume of solid product of hydration of cement=31.8+0.23 X 100 (1-0.254)
The cement paste at this condition has characteristic porosity around=28%That is
Where wg=volume of gel water
Thus the volume of hydrated cement paste=48.9+19=67.9 ml
The summary of the example 1 can be drawn as in table-1
From table -1 it can be concluded that
Total volume of water in the mix=23+19=42 ml
Water/cement ration= 42/100=0.42 (by mass)
Water/cement ration= 42/31.8=1.32 (by volume)
Actual volume cement+water=31.8+42=73.8 ml
Volume reduction during hydration=73.8-67.9= 5.9 ml
Volume of hydration products for 1 ml of dry cement=67.9/31.8=2.13 ml
volume or volume occupied by unit mass of cement
wo=volume of water in the mix
If specific volume of cement in dry state is considered 0.319 ml/gm above equation becomes
Relation between strength and water/cement ratio
we know a reasonably low water/cement ratio will produce more strength, Too low water cement ratio may reduce workability and may supply insufficient water to hydrate significant fraction of cement incorporated in the mix. A too high water/cement ratio produces a porous structure leaving concrete of inferior quality both strength and durability point of view. But this relationship with water/cement ratio does not based on a well constituted law as water/cement ratio rule cannot be validated by proper qualification.
Strength of concrete at any water/cement ratio depends on other factors like
Physical and chemical properties of cement
- Degree of hydration of it
- Ambient environment around hydration process like air content in the concrete and temperature.
- Change in effective w/c ratio
- Crack formation due to bleeding
- The cement content in the mix
- Properties of interface between aggregate cement paste
Relation between strength and gel-space ratio
|Figure-2: Relation between development of
strength and gel/space ratio of mortar
From the figure-2, it is noticed that strength has approximate proportionality with cube of gel/space ratio and he figured out that 234 Mpa was the inherent strength of gel for that type of cement and specimen examined at that time. For usual Portland cement we used in our construction works, the numerical vales were found more or less same; some exceptions are observed for cements having higher C3A content as they yield lower strength at a particular gel/space ratio.
Correction for specific gravity of adsorbed water
Why specific gravity of adsorbed water is 1.1?
What is disjoining pressure?
An investigations applying nuclear magnetic resonance showed that gel water required same energy to make bond as that remain in interlayer water of some expansive clays; thus is can be said that gel water is a form of interlayer water. The non-evaporable water calculated in example 1.0 comprises approximately all chemically bonded water and some water that is not chemically bonded. Such water remains in lower vapor pressure than the pressure of the surrounding atmosphere; thus quantity of this water may vary depending on ambient vapor pressure.The energy of binding water in cement paste depends on the manner of holding water in it; as an example to establish bond of 1gm non-evaporable water 850 calories (1670J) are used and energy required to crystallize 1 gm water of Ca(OH)
2 is 850 cal (3560J).Similarly the specific gravity of water taken as 1.2 in case of non-evaporable water and this value is 1.1 for gel water and 1.0 in case of free water as usual.
Don’t be confused about the increase in density due to compression at low surface concentrations; the actual cause is the ordering or orientation of the molecules of water in the adsorbed phase under the action of surface forces which results a pressure called disjoining pressure.
This pressure is required to maintain the film of adsorbed molecules of water against external influence.
Thus the calculation of gel/space ratio requires a little modification to encounter revise specific gravity of water. Therefore the actual situation is that volume of pores will be larger to some degree as we assumed.
Correction for air content
If the volume of air exists in the cement paste is A, the equation (2) the ratio of W0/C will be replaced by
|Figure-3: Relationship between compressive
strength and gel/space ratio of mortar with
correction for entrapped air.
Where C, w and a represents absolute volumetric proportions for cement, water and air respectively
Simplification of relationship
The expression for relationship between strength and gel/space ratio can be used in several ways. For simplification and convenient to use consider
• Wn α volume of gel, when wn=non-evaporable water in the mix.
• W0 represents available space for the gel
The expression for strength can be written as follows when fc in psi fc>2000 psi
Equation (5) shows a linear relationship.
An alternative expression can be written in terms of surface area of gel vm.
Figure-4 was established by power (1947) based on actual data for cement having low C3A content.
|Figure-4: Relationship between the strength of cement paste and the ratio of surface area of gel Vm to the volume of mixing water w0|
Effect of temperature on gel/space ratio
Thus high density of hydration product is produced in vicinity of particles still waiting for hydration reaction or in state of some degree of hydration and inhibit subsequent hydration. As a result gel/space ratio will be less in the interstices and adversely affects strength of concrete in the long run. Thus the local weakness in the concrete section will permit to progress cracks and results a lower strength of it as a whole. With the help backscattered electron imaging it has been confirmed that porous C-S-H exist in between hydrated cement particles.
Influence of chemical composition of cement
As per chemical composition, only gypsum content of cement is here prime concern. For a given cement, the gypsum content defines shrinkage and setting time of cement; but the gypsum content that is satisfactory in respect of shrinkage is found not adequate for establishing desired setting time. Gypsum is added to cement clinker during manufacturing process of cement and then final grinding of clinker is done. As discussed in above section about temperature, the initial structure produced during setting determines structure of cement paste at upcoming stages of hydration. Thus gel/space ratio is dependent on optimum gypsum content to facilitate hydration of as much as cement particles to gain strength and behavior of concrete under shrinkage and creep are also affected.
Advantages and disadvantages of gel/space ratio expression
The strength correlation with W/C of concrete is applicable for particular type of cement, at the age of strength prediction and also set under specific curing conditions (wet curing). In contrast to that strength-gel/space ratio correlation furnishes more generalize application as volume of gel production within the cement paste after any time of placing is itself a function of type of cement and age. The gel-space expression thus accounts for the fact that different amount of gel can be produced at a same amount length of curing for application of different type of cement.
Gel/space ratio to strength relationship is found to be applicable for may type of cements, but the numerical co-efficient used in equation (5) and (6) are often dependent on the inherent strength of gel produced from hydration of a particular cement. In simple word, the strength of cement paste depends mainly on physical structure of gel formation; but have some influence of chemical properties of cement which will be diminished with time. Another way to determine the properties of the gel is to find relation between strength and porosity. But this method has also limitation as it is affected by bonding capability of the material i.e. having resistance to propagate crack through it. A poor bonding between adjacent crystals can be outcome of easy path for propagating cracks.