A jackhammer is your best tool for breaking through the asphalt. The ground typically features a thick layer of asphalt applied over a softer soil. Sometimes the installer lays gravel or sand between the soil and asphalt, which grips the asphalt better than soil alone. You must break the asphalt into smaller chunks or pieces before adding your fence posts. A jackhammer quickly breaks up the material due to the pressure and force against the surface.
Consider using a circular saw with a diamond blade before employing the jackhammer. The diamond blade cuts through the surface of the asphalt without damaging the surrounding areas. Before using the blade, mark the location of the hole for each fence post. Run the saw around the mark, applying more force each time you circle around the hole. Eventually, you'll break through the upper layer of the asphalt, leaving the surrounding areas intact. A regular hammer or jackhammer applied to the area will break the asphalt, letting you remove it from the hole.
Always wear protective gear, including goggles, when using power tools. The gear protects your face, eyes and body from damage. As you break the asphalt, small and large chunks might fly through the air, causing damage to you or anyone nearby. Be careful in regard to the surrounding area. Even minor cracks in the surrounding asphalt can ruin the look of the fence. The cracks can lead to chipping and splitting with chunks of asphalt breaking off the ground.
After breaking and removing the asphalt, mix the concrete. A small amount of concrete poured in the hole offers some support once you place the fence post in the hole. Add more concrete until it reaches the top of the hole, wipe off any excess concrete and let it dry overnight. The concrete hardens and keeps the fence post from toppling over, while also offering support for the fence. Wipe the concrete off the surrounding asphalt before it dries and hardens.