In this paper we present a new family of Intensional RDBs (IRDBs) which extends the traditional RDBs with the Big Data and flexible and 'Open schema' features, able to preserve the user-defined relational database schemas and all preexisting user's applications containing the SQL statements for a deployment of such a relational data. The standard RDB data is parsed into an internal vector key/value relation, so that we obtain a column representation of data used in Big Data applications, covering the key/value and column-based Big Data applications as well, into a unifying RDB framework. We define a query rewriting algorithm, based on the GAV Data Integration methods, so that each user-defined SQL query is rewritten into a SQL query over this vector relation, and hence the user-defined standard RDB schema is maintained as an empty global schema for the RDB schema modeling of data and as the SQL interface to stored vector relation. Such an IRDB architecture is adequate for the massive migrations from the existing slow RDBMSs into this new family of fast IRDBMSs by offering a Big Data and new flexible schema features as well.