If your home and outbuildings are in the midst of rock chuck habitat, which must be the case, then permanent eradication won't be feasible. 
However, you can manage the habitat on your property to reduce its quality for the animals, and also exclude them from getting under the buildings. 
For starters, the rock mound on your property sounds like perfect natural habitat structure to host and protect rock chucks. If it is possible to eliminate that feature, production of new rock chucks would likely fall. Alternatively, you could consider fencing to exclude the animals from the area immediately around your cluster of buildings and thus block the rock-mound animals from getting into your protected area. Not knowing the relative scale or layout of the property, it's hard for me to say whether that approach would be best. If you decide to fence out rock chucks, you'll need to trench at least 12-18" deep and likely that wide, and then lay welded wire/hardware cloth (NOT chickenwire) in an undiggable L-shaped apron before back-filling. The metal fence then needs to be attached (no gaps) or extended 3-4 feet above-ground. Despite their chunky shape, marmots can be surprisingly good at climbing, and I have seen others recommend using a single electric wire at the top or extended a few inches outside the top of fences to prevent the over-topping by ambitious climbers. Another alternative to consider, although I haven't seen this option trialed, would be to do the underground portion of the fence and then top with electrified poultry fencing (like a net). You could check with neighbors to see if any have had success with that tool before you try it. 
If your buildings are widely distributed, then excluding the rock chucks from underdigging the foundations is likely going to need a contractor's expertise to trench around and then place corrugated metal sheeting or some other undiggable barrier around each structure. 
Rock chucks eat grasses, forbs (e.g., wildflowers and sub-shrubs), and some seeds, but they unfortunately also can learn to take advantage of foods we humans inadvertently provide, such as silage, garbage/garden waste, spilled bird seed or pet chow, etc. So reducing the food available immediately around your buildings will be important to reduce the overall carrying capacity and allure of the area from the animals' perspective.
Once you have secured the perimeter of whatever area you're going to protect, eliminate animals within with Conibear-style body-gripping traps. Be very, very careful in place those however, because they are lethal to whatever trips them, and unfortunately people sometimes accidentally kill their own pets, non-target wildlife, or small livestock due to poor siting.