In general, it will depend on your insurance carrier. Your homeowner's insurance may cover an ice heave but that is something you will have to check on. Ice heaving is a special consideration that is unique to your specific location, state, or region. Most homeowner's insurance does cover ice damage up to a certain extent but whether an ice heave qualifies as ice damage it up to your specific provider. As it does not occur regularly on a national level mainstream insurers may not cover it at all.
The first thing you should do is check your policy. You can do this with a call to your agent or by looking over the policy itself. If you are lucky it may be covered as it is a common occurrence for your area, or may even qualify under the guise of ice damage. If not, it may be available in the form of extra coverage.
Local homeowners insurance probably has a better chance of offering coverage as they have a better understanding of the area. So if your policy belongs to a local company you probably fare better. Most likely any coverage available for heaving will be an extra charge.