Novel periodic pile barrier with low-frequency wide bandgap for Rayleigh waves

•The combination of the sound cone method, energy distribution parameter method, and vibration mode identification can effectively capture the pure surface wave mode and leakage wave mode of the periodic barriers.•The influences of the shape of the inclusions section on the surface wave bandgap and leakage wave mode with the same filling ratio are clarified.•The influences of barriers with various inclusions on the initial frequency and bandwidth of the surface wave bandgaps are discussed and beneficial to the filling materials and selection.•The transmission model of the finite barriers further verifies that the leaky mode inside the sound cone is conducive to expanding the attenuation frequency range.