We analyze radiation from a filamentary bunch that uniformly moves in a circular waveguide and crosses the boundary between two areas: the one has a corrugated wall and another has a smooth wall. It is assumed that the corrugation period is much less than the wavelengths under consideration. However, in difference with our previous works, the corrugation depth is of the same order as the wavelength. The influence of the corrugation on the electromagnetic field is investigated using the method of the equivalent boundary conditions. At first, we study a regular corrugated waveguide. Then two cases of the waveguides with boundaries between the corrugated and smooth regions is studied: first, when the bunch flies out of the corrugated part into the smooth one, and second, when the bunch flies into the corrugated part from the smooth one. We obtain and analyze the analytical expressions for the field components in both areas and reveal the main physical peculiarities of the bunch radiation.