You have received good advice in many of the posts above.
The indirect effect of many small changes in disrupting a project is well documented in many industries. Many large defence contractors seem to feed off delay and disruption claims against their client (the government = the taxpayer = us).
But even in the real world, this effect does exist and is often much greater than the direct cost of the change if considered in isolation.
But it is hard to prove.
One journalistic account of a major project gone wrong because of late and changed design (and other factors) is RUNNING CRITICAL, by Patrick Tyler. It is about Hyman Rickover and the US Navy design for the Los Angeles class submarines, General Dynamics Corporation and their Electric Boat shipyard where they were built. It is about many things, but delay and disruption is one of them.
If nothing else it will make you feel relieved to know that other people have gone through even greater project catastrophes than your own (although that can sometimes be hard to believe).
SYSTEMS DYNAMICS or feedback dynamics is one area whose practioners claim can provide the proof. But these consultants are expensive.
Here are some professional references which might not be of much practical use but they (and THEIR references) will indicate to you that the literature is HUGE.
Eden et al
THE ROLE OF FEEDBACK DYNAMICS IN DISRUPTION AND DELAY ON THE NATURE OF DISRUPTION AND DELAY IN MAJOR PROJECTS
Journal of the Operational Research Society (2000). 51, 291-300
Kumaraswamy
SUBSTANTIATION AND ASSESSMENT OF CLAIMS FOR EXTENSION OF TIME
International Journal of Project Management, 21 (2003) 27-38, Pergamon Press
Williams
ASSESSING EXTENSION OF TIME DELAYS ON MAJOR PROJECTS
International Journal of Project Management, 21 (2003), 19-26, Pergamon Press
Cooper
NAVAL SHIP PRODUCTION - A CLAIM SETTLED AND A FRAMEWORK BUILT
Interfaces, Vo. 10, No. 6, Dec 1980. Institute of Management Sciences, Dec 1980