Bitcoin-based smart city services are an ever increasing up-and-coming reality. For these services, simulating the Bitcoin blockchain is important to parametrize the system and tailor the costs and the economic incentives. In this regard, SimBlock simulator is the current state-of-the-art tool for blockchain simulations. Unfortunately, based on an up-to-date parametrization, SimBlock turns out not to simulate the mining of blocks. Furthermore, it does not simulate the incentive mechanism. These limitations strongly confine SimBlock's effective usage towards evaluating Bitcoin-based services relevant to many application contexts, including smart cities. To overcome these limitations, we propose an improved SimBlock's implementation. Upon it, we assess whether SimBlock can abstract the current Bitcoin blockchain. The experimental analysis shows that the proposed implementation can effectively simulate the current Bitcoin blockchain. Though, introducing relay network modelling in SimBlock should even improve the accuracy of the simulation.