the contract notes about culverts being put in. and broad base.
the seller already has noted he would come back and do that after the rains show the bad spots.
the contract noted 50/50 with a max of 5,000 max per party for a total of $10,000
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at this moment in time, it sounds like ya left it all up to the contractor. without doing your homework before hand. if ya want things done right. i would say grab a hold of the rings. and keep on everything and keep communication going between you and the seller.
if you are not able to easily look things over, request multi pictures and/or video.
get your own bids, and talk to local contractors, not just the one that originally did the work. open up the local phone book for area. ((not internet)) and look up "dirt", "excavation" and like. i say actual paper phone book, due to many times, ad's folks place, show up in paper phone book vs internet, that can give you some better info of who to call first. and then goto internet yellowpage websites. and search 100 or so miles further away. and contact some contractors. there will be slightly higher freight charges for shipping the equipment in, but perhaps lower overall bids.
also look into DIY the road, meaning buying machinery or implements or what not and see about doing it yourself. even if you do not do this. many times you can pickup very good info and those little tid bites of info that really help. i honestly do not like referring folks to local library books, but roads have been around for years. and a book might give you better pictures, and descriptions vs some internet web guide.
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get a game plan / list of what other things need to be done on property.
would a backhoe or excavator, work better than say getting another dozer in there, or running rear blades and box blades, or a road grader?
when just looking at pictures, myself it would be a backhoe. you have a rough cut road. with rock already down. i would be hesitant in pulling dirt on high side of drive to the lower side of drive. to put in culverts and ditches. but it also could come down to. try to re scrape the rock up. and taking loss on some gravel. i say larger size backhoe. so you can set almost in center of road way. and take buckets full of dirt from high side, and swing the backhoe to lower side of drive. and then come back with the FEL and push the dirt down the lower side hill.
it has been some time since i have seen them. but there is 3pt ditchers. that hook up to larger size tractors. that can send the dirt up into a truck. or shoot the dirt off to another side.
never used a pull behind scraper. (kinda like a box blade) but a lot more capacity to get dirt. might be a way to get your culverts in. without dragging dirt right across the current rock.
perhaps getting a 1 or 2 bottom plow, and hitting the ditch areas, and then running the FEL into the softer torn up dirt. and moving it to lower side. then cleaning things up with rear blade and box blade.
compare your little tractor to say a older TLB (tractor loader backhoe) or bigger sized older tractor if DIY, and get major work done. then come back with your little tractor and do touch ups and maintenance with.
everything can be done multi ways, what makes sense to you?