One of the most important features of microblogging services such as Twitter is how easy it is to re-share a piece of information across the network through various user connections, forming what we call a «cascade». Business applications such as viral marketing have driven a tremendous amount of research effort predicting whether a certain cascade will go viral. Yet the rarity of viral cascades in real data poses a challenge to all existing prediction methods. One solution is to simulate cascades that well fit the real viral ones, which requires our ability to tell how a certain cascade grows over time. In this paper, we build a general time-aware cascade model for each particular cascade, in which the chance of one user's re-sharing behaviour over time is modelled as a hazard function of time. Based on two key observations on user retweeting behaviour, we design an appropriate hazard function specifically for Twitter network. We evaluate our model on a large real Twitter dataset with over two million retweeting cascades. Our experiment results show our proposed model outperforms other baseline models in terms of model fitting. Further, we make use of our model to simulate viral cascades, which are otherwise few and far in-between, to alleviate the imbalance issue in cascade data, offering a 20% boost in viral cascade discovery.