A three-dimensional displacement discontinuity method for crack problems in layered rocks

A new displacement discontinuity method (DDM) is developed for the analysis of crack problems in layered strata. This approach is based on the fundamental solution of multilayered elastic solids. The discontinuous displacements of crack surfaces are treated as unknown quantities. In developing the DDM, discontinuous elements and special functions are applied to describe the variation of discontinuous displacements. The numerical method is used to calculate the hypersingular integral in the integral equation. Then, the numerical verification shows that the present results are in very good agreement with the existing ones. Finally, the proposed method is used to analyze the square crack in layered rocks, which consist of fine-grained sandstone and mudstone. The stress intensity factors (SIFs) are obtained for different cases including uniform and non-uniform loads. The results show that the heterogeneity of layered strata exerts a clear and quantitative influence on the SIFs of the cracks in layered rocks.