Based on the kinematic approach of the limit analysis and slip-line theories, this paper proposes a new 2D analytical model to evaluate the collapse support pressure to ensure the face stability of a circular tunnel in purely cohesive soils driven by a shield. The normality conditions, the yield criterion and the vertical soil arching effect are considered in the analytical model. Two upper bound solutions corresponding to the ratio of the cover to the diameter (C/D) are derived from considering the mechanisms based on the motion of rigid multi-blocks. Comparisons are made with existing upper and lower bound solutions published in previous articles. The results are close to the solutions of practical engineering. The failure mechanisms proposed in this study provide a better explanation for the failure process in the heading of the tunnel face.

Consensus algorithms are the core technology of blockchain and a focus in the current distributed system research. The consensus algorithms are widely used in distributed systems, it has solved the decentralization problem. The traditional consensus algorithm needs the process of node legitimacy checking, identity authentication, and primary node view change, so the time cost of reaching an agreement between nodes is still exponential. In response to the problem, a lightweight consensus algorithm based on graph (LCAG) is proposed for the Internet of Things (IoT) in this paper, which is proposes an access control table, and reaches an agreement among nodes by calculating the probability of nodes in the control table, and reduces the time overhead of the reaching an agreement in distributed systems. We have carried out simulation experiments for the new algorithm, and the experiments show that: the new algorithm needs less time overhead than the classical Byzantine algorithm need, as well as Byzantine Generals problem (BGP), practical Byzantine fault-tolerant algorithm (PBFT) and directed acyclic graph (DAG) algorithm, and so on. The new algorithm can be applied to the devices of IoT, which have limited computing power.