Is it obligatory for me to fast two consecutive months as expiation for the death of an engineer who was crushed by an excavation site I was supervising, despite my warning him and taking all engineering precautions?

If you had not warned the engineer about the danger of excavating at this site, you would have been liable for what happened to him, because failing to warn is considered an act related to your responsibility. However, since you explicitly warned him and ordered him to stay away, there is no liability upon you unless you could have rescued him after the the site collapsed and you failed to do so.