Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses

A new multiscale numerical model in which the coordination between the internal boundary (such as cracks and holes) and meshes is not necessary for simulating the damage evolution of crack-weakened rock masses is proposed based on the extended finite element method and global–local analysis. The connection between different sizes of meshes behaves smoothly through combining the displacement projecting method and displacement loading method. The contact constraint on crack surfaces is embedded within the total stiffness matrix using the penalty method. The path of crack propagation and stress fields are determined through iterative computations. Because additional discontinuous functions and enriched tip elements are added into the displacement field, the geometry of cracks is independent of the finite element mesh. As a result, re-meshing is not necessary to model crack propagation using the present new model. As the frictional contact of crack surfaces is taken into account, the present method is suitable for modeling the growth and coalescence of multiple cracks in geomaterials under compressive loads as well as tensile loads. Finally, the present method is employed to simulate multiple cracks growth when frictional contact exists on the crack surfaces. Comparison between the numerical and experimental results shows that the present numerical results are in good agreement with the experimental ones.

► The contact constraint on crack surfaces is embedded within the total stiffness matrix using the penalty method.
► The path of crack propagation and stress fields are determined through iterative computations.
► The geometry of cracks is independent of the finite element mesh.
► Method is suitable for modeling growth and coalescence of multiple cracks in geomaterials under compressive and tensile loads.