Surface wave propagation in a half‐space with a single set of regular joints

Abstract

The dispersion of surface waves is investigated herein for a half‐space of a jointed rock medium with a single set of regular joints with an arbitrary angle between the free surface and the joint plane. The intact rock layers are assumed to be linearly elastic, and the joint response is prescribed by linear traction‐slip relations. Since the exact surface wave analysis of the jointed half‐space is difficult due to a multitude of joints in the domain of the analysis, a high‐order homogenization model, proposed by Murakami and Hegemier (1989) is adopted. The model incorporates accurately the harmonic wave dispersion in a jointed full space and is capable of predicting the surface wave propagation down to the wavelength of the order of approximately two intact layer thicknesses. For a jointed half‐space with the angle between the joint plane and the free surface less than approximately 30° the surface wave phase velocity spectra is found to exhibit dramatic dispersion. The surface wave velocity increases as much as 87% for the angle 0° and 39% for the angle 30° as the wave number or frequency increases. This dispersion characteristic of the surface wave is due to the dispersion of plane shear waves in a jointed full space in the waveguide direction. The effect of surface wave dispersion in the time domain has been investigated by solving Lamb's problem under plane strain. A jointed half‐space with joint planes parallel to the free surface has been analyzed by the finite element method. The time history of velocity and displacement at different observation points exhibits spreading of waves due to dispersion. Surface wave in a half space covered by a solid layer with lower shear wave velocity exhibits the phase velocity reduction with the wave number. It is interesting to note that the surface wave dispersion observed in jointed half‐spaces with joint angle between 0° and 30° exhibits the opposite trend.