In a virtualized data center, survivability can be enhanced by creating redundant Virtual Machines (VMs) as backup for VMs such that after VM or server failures, affected services can be quickly switched over to backup VMs. To enable flexible and efficient resource management, we propose to use a service-aware approach in which multiple correlated VMs and their backups are grouped together to form a Survivable Virtual Infrastructure (SVI) for a service or a tenant. A fundamental problem in such a system is to determine how to map each SVI to a physical data center network such that operational costs are minimized subject to the constraints that each VM's resource requirements are met and bandwidth demands between VMs can be guaranteed before and after failures. This problem can be naturally divided into two sub-problems: VM Placement(VMP) and Virtual Link Mapping (VLM). We present a general optimization framework for this mapping problem. Then we present an efficient algorithm for the VMP sub problem as well as a polynomial-time algorithm that optimally solves the VLM sub problem, which can be used as subroutines in the framework. We also present an effective heuristic algorithm that jointly solves the two sub problems. It has been shown by extensive simulation results based on the real VM data traces collected from the green data center at Syracuse University that compared with the First Fit Descending (FFD) and single shortest path based baseline algorithm, both our VMP+VLM algorithm and joint algorithm significantly reduce the reserved bandwidth, and yield comparable results in terms of the number of active servers.