Wireless Data Center Network (Wi-DCN) is considered one of the most promising future data center architectures due to its low installation and management cost and high flexibility of network design. However, the existing Wi-DCN is, still, not capable of providing an efficient big data mining service such as MapReduce because its topology (i.e., Cayley graph with same degree) cannot achieve enough connectivity on the breakdown of servers and spectrum efficiency, which are important factors to improve the performance of big data mining. Therefore, in order to modify the existing Wi-DCN for big data mining, this paper proposes a spherical rack architecture based on a bimodal degree distribution that improves both failure tolerance and spectrum efficiency. Extensive computer simulations demonstrate the effectiveness of our proposed rack architecture in terms of data transmission time required for MapReduce under a failure-prone environment.