Underground mining is an industry that preserves the miners' safety and efficiency in their work using wireless communication systems as a tool. In addition to communication links characterized by radio frequency signals, optical links in the visible light spectrum are under intense research for underground mining applications due to their high transmission rates and immunity to electromagnetic interference. However, the design of a robust visible-light communication (VLC) system for underground mining is a challenging task due to the harsh propagation conditions encountered in mining tunnels. To assist researchers in the design of such VLC systems, we present in this paper a novel channel model that incorporates important factors that influence the quality of the VLC link in underground mines. Features such as an arbitrary positioning and orientation of the optical transmitter and receiver, tunnels with irregular walls, shadowing by large machinery, and scattering by dust clouds are considered. These factors are integrated into a single modeling framework that lends itself for the derivation of compact mathematical expressions for the overall DC gain, the impulse response, the root mean square delay spread, and the received power of the proposed VLC channel model. Our analytical results are validated by computer simulations. These results show that the rotation and tilt of the transmitter and receiver, as well as the tunnels' irregular walls have a notorious influence on the magnitude and temporal dispersion of the VLC channel's line of sight (LoS) and non-LoS components. Furthermore, results show that shadowing reduces the LoS component's magnitude significantly. Our findings also show that scattering by dust particles contributes slightly to the total VLC channel gain, although it generates a large temporal dispersion of the received optical signal.