The mechanical characteristics and orientation of joints determine the behaviour of rock masses, including the strength, the stiffness, and all forms of conduction and diffusion. Furthermore, the preferential orientation of joints renders the medium anisotropic. In turn, these properties affect the velocity and damping of propagating elastic waves. The purpose of this study is to investigate the propagation of long-wavelength shear waves through a rock mass with open joints filled with softer gouge, and subjected to low confinement. These conditions are selected in view of near-surface geophysical characterisation studies for geotechnical engineering applications such as foundations, tunnels and slopes. Experimental data are gathered with a slender column made of discrete elements with gouge material in the joints. The column is excited in the first torsional vibration mode to gather accurate measurements of velocity and damping for wave propagation direction normal to the joints. Data are analysed with mixture models. The potential use of wave propagation methods to assess jointed rock masses is discussed.