Calculation of C3S for pure OPC cement

Free lime does not participate in the formation nof c3s.
Therefore, the Bogues formula should be used after deducting free lime.

Another point of view is simply to go back to the origin of the Bogues formula.
The Bogues formula are the solution of the linear equations relating the given analysis {CaO, SiO2, Al2O3, Fe2O3} to the unknown {c3s, c2s, c3a, c4af}.

If you assume that a given amount of free lime will occur, then the Bogue formula must be modified to become the solution of the equation that relate {CaOfree, CaO, SiO2, Al2O3, Fe2O3} to the unknown {CaOfree, c3s, c2s, c3a, c4af}. The result is again that you have to deduct CaOfree.

Same reasoning, I guess, for the IR.
(assuming IR components do not participate in the main phases)

Of course, this all theoretical, assuming ideal phases.
If CaOfree or the IR are soluble in the c3s phase, for example, then the % amount of the phase observed experimentally will differ from the Bogue calcualtions.
The calculations could be refined, but they would need data on the actual phases formed.
This would amount to calculate knowing the experimental answer.

BR

Michel

For calculating C3S in OPC a factor for SO3/Gypsum correction comes into picture. so modified C3S formula for OPC becomes: 

4.071*(CaO-fCao)-7.6*SiO2-6.718*Al2O3-1.43*Fe2O3-2.852*SO3