Just leave them alone leave them there take look again after next season, sometime drain line over dry out soil. Blackberries die wet weather some drown in winter die when warm up because water kills roots.

Why, you worried about roots clogging drainage?

I have planted orchards in drainage fields and clients suffered no consequence after 10 years but where I live there are usually large trees with roots extended into drainage fields anyway.

We have to follow very stringent rules with our septic systems in this part of the world when we replace them. This means it is very expensive - $25,000 for a small house. So I don't want to allow anything to damage it! Since it is to the west of the berries and it appears they travel east when left to their own devices, I'm not too concerned about the roots. Just damage done by the contractors. Admittedly, these blackberries are weeds so will probably survive the experience!
Thanks for the advice, guys.

I agree they are likely to survive, but those 15,000 pound or more bobcats running over the ground compressing the soil is enough to kill anything.

I assume they are reasonably extensive. If you can wait until they are dormant then do so---IF you can dig into the ground at that time of year. Otherwise consider digging up and temporarily potting two or three pots worth of rhizomes (root cuttings) and get them overwintering in a garage as a security precaution to plant them in the spring if necessary.. Hopefully they won't be needed, but....

Preserving a chance GOOD blackberry already proven in your environment is a smart thing to do.

Here is a link that might be useful: root cuttings