Construction waste hauling trucks (CWHTs), as one of the most commonly seen heavy-duty vehicles in major cities around the globe, are usually subject to a series of regulations and spatial-temporal access restrictions because they not only produce significant NOx and PM emissions but also causes on-road fugitive dust. The timely and accurate prediction of CWHTs' destinations and dwell times play a key role in effective environmental management. To address this challenge, we propose a prediction method based on an interpretable activity-based model, input-output hidden Markov model (IOHMM), and validate it on 300 CWHTs in Chengdu, China. Contextual factors are considered in the model to improve its prediction power. Results show that the IOHMM outperforms several baseline models, including Markov chains, linear regression, and long short-term memory. Factors influencing the predictability of CWHTs' transportation activities are also explored using linear regression models. Results suggest the proposed model holds promise in assisting authorities by predicting the upcoming transportation activities of CWHTs and administering intervention in a timely and effective manner.