Building Information Modeling (BIM) is envisioned as an indispensable opportunity in the architecture, engineering, and construction (AEC) industries as a revolutionary technology and process. Smart construction relies on BIM for manipulating information flow, data flow, and management flow. Currently, BIM model has been explored mainly for information construction and utilization, but rare works pay efforts to information security, e.g., critical model audit and sensitive model exposure. Moreover, few BIM systems are proposed to chase after upcoming computing paradigms, such as mobile cloud computing, big data, blockchain, and Internet of Things. In this paper, we make the first attempt to propose a novel BIM system model called bcBIM to tackle information security in mobile cloud architectures. More specifically, bcBIM is proposed to facilitate BIM data audit for historical modifications by blockchain in mobile cloud with big data sharing. The proposed bcBIM model can guide the architecture design for further BIM information management system, especially for integrating BIM cloud as a service for further big data sharing. We propose a method of BIM data organization based on blockchains and discuss it based on private and public blockchain. It guarantees to trace, authenticate, and prevent tampering with BIM historical data. At the same time, it can generate a unified format to support future open sharing, data audit, and data provenance.