Rotating drums are extensively used in the chemical and process industries as mixers, dryers, granulators and reactors for processing granular materials. As a result, granular behaviour in rotating drums has attracted numerous research efforts from both engineering and physics communities over the past few decades. Most of these studies have been focused on drums operated in or close to the rolling mode. However, there are many industrial cases where drums are operated in other modes, e.g. the cascading and cataracting modes, which forms the main motivation for this work. Comprehensive experiments have been carried out to investigate granular behaviour in a drum operated over a wide range of rotational speed with solids motion across the rolling, cascading and cataracting modes. A digital recording device was used to capture images of the transverse plane of the material bed. Analyses of the images were carried out to extract the bed behaviour as a function of rotational speed, drum fill level and particle size. This has led to three relationships between the surface shape expressed in terms of three characteristic lengths, operating conditions, as well as the friction properties of both particles and drum wall. These relations are found to apply approximately to the whole range of rotational speed used in this work. The generality of these relationships and possible application of them for drum scaling are discussed.