What would be the effects of embedded pvc plumbing pipes to concrete strength? and in any case do you have reports on this research that I may refer to as am carrying out more on the same topic

It is done all the time in construction. Every slab on grade house has embedded PVC in the concrete. However, your question is a bit vague. Pre cast, post tensioned? Slab on grade, tilt wall? Lots of types of concrete construction.

You asked this under Grad School. This site isn't a reference library for grad students, although there are plenty of experts in the building trades. You need to research this on concrete sites and schools of architecture, etc., because you need a lot of in-depth information. You could write a whole book just on the nature of concrete, which changes gradually over long periods of time, so you have to be fully informed on that first.

Just off the top of my head I recall reading that concrete becomes more porous for the first 40 years. That implies some shrinkage, and if pipe of any kind is embedded in it, then the pipe is no longer providing support, and thus the concrete does lose some integrity. Then there's the matter of vertical vs horizontal. I'm sure there's more, such as expansion and contraction of PVC.
This will need a lot of research. We do some for people, but not whole topics for school.