I think the first objective when CNTs were incorporated in cement matrix was to serve as a nano-scale fiber reinforcement. Altough there are some promising results, there is very few evidence of such behavior. An other effect that should be expected of CNT addition is an impact on the cement hydration process and hydration product formation. Since every reaction happens on surfaces, the addition of a high surface area material will obviously affect those reactions. In this case the functional groups present on CNT surface, the dimensions and morphology of CNTs and the effectiveness of dispersion will be the main variables to describe the influence. Alteration of the cement hydration products will also impact their mechanical parameters. But the alterations occure only in cement paste phase. Since in concrete you have also aggregates, the effects on mechanical behavior of the whole composite is a very complex question.
Have a look at my publications for some results on mechanical behavior of CNT-cement composites