Role-based access control (RBAC) has attracted considerable research interest. However, the computational issues of RBAC models are yet to be thoroughly studied. In this paper, we study the problem of efficient maintenance of large RBAC models in a database-based multi-domain Web service environment. We propose first-order (SQL) algorithms to maintain the reachability of access roles under dynamic changes. The main advantages of our algorithms are: the support of various operations required for managing access roles with fractional information of roles; the maintenance of an update through operating a bounded number of join operations despite of the data size. To the best of our knowledge, our algorithms are the first attempt to maintain RBAC models using a first-order language.