A continuum finite element for single‐set jointed media

Abstract

AbstractIn response to the need for an advanced computational model for wave propagation in jointed‐rock media a new finite element for jointed media with a single set of regularly spaced joints is developed. The element is a numerical implementation of the higher‐order homogenization model recently proposed by Murakami and Hegemier. Due to the dispersive effects induced by regularly spaced joints, wave phenomena in jointed media are altered significantly. Therefore, in order to improve the interpretation of seismograms for accurate source identification, it is necessary to develop a higher‐order continuum element. The accuracy and efficiency of the new element is investigated by applying it to wave‐guide and wave‐normal problems of a jointed half‐space and by comparing the wave response with that of DYNA2D. The analyses by DYNA2D discretize explicitly the details of the joint microstructure, and are adopted as numerically exact measures for the assessment of the proposed finite element; good correlations were obtained. The validation study also confirmed the importance of wave dispersion for non‐linear as well as linear joint responses. Finally, as a more practical application of the proposed element, the problem of a jointed full‐space with a cylindrical cavity pressurized by step and pulse loadings was solved. Velocities at several observation points were compared with the numerically exact results of DYNA2D. Similar analyses carried out for elastic isotropic media predicted totally different velocity responses and confirmed the need for the proposed element.