wolfhnd,
I have to admit that after reading you latest post, a different light is shed on your question. My first reaction was to suggest writing into the specifications the requirement that the contractor hire a geotechnical firm to do the required monitoring. That way the costs of the monitoring become part of the construction cost rather than the design cost, just as you suggest.
But then I wondered how do YOU decide what the parameters of the monitoring are going to be without first having a geotechical firm tell you? (Bye the way, from what you said in your first post, I would change geotechs!) If that is the case, just leave the whole thing back in the design phase. The monitoring effort should be part of the ongoing project inspection costs and you preserve the "arms length" relationship between design and construction.
This may seem harsh, but I am always skeptical of an Owner who has enough money to do the construction phase, but not enough money to do the complete design or construction inspection phases. In the end, it ALWAYS costs someone more than it should when things are done skimpy.
One last suggestion, can you put in dewatering wells or a cutoff wall to dewater the area?