This study experimentally explores the propagation mechanisms of acetylene/air detonation waves within a channel intermittently constrained on one side, utilizing soot foil and high-speed schlieren photography to capture the cellular structure and shock-flame evolution. The experiments revealed that the detonation waves traverse the semi-enclosed channel with various discrete wall configurations on the side in three distinct propagation modes: (I) periodic detonation failure and re-initiation; (II) single extinction and re-initiation; (III) non-extinction. Mode I occurs exclusively when the open area ratio exceeds 0.85, while detonation tends to favour Mode II when the gaps between discrete walls exceed three times the cell size; otherwise, it tends towards Modes III. The re-initiation mechanism of detonation involves curvature shocks inducing local explosions of reactive mixtures through multiple Mach reflections off the discrete walls. The self-sustained propagation mechanism of the detonation wave is maintained by the interaction of strong transverse shocks reflected from discrete walls with the inherent transverse waves within the detonation structure, sustaining the instability of the cellular detonation.