A large number of real rock and model material experiments and numerical simulations on the mixed mode fracture under compression-shear loading had been carried out by scholars at home and abroad. However

due to the discreteness of the test results and lack of influencing factors research on the test results

also the conventional finite element method has many difficulties to deal with the strong discontinuities

such as the crack

we need to make a high density mesh on the crack tip which is the stress focus zone

also

we need to remesh as the crack grows

it is complicated and low efficiency

so

little satisfactory results on mixed mode fracture under compression-shear loading experiments were obtained. Therefore

a theoretical and numerical analysis were carried out to investigate the influence of geometric characteristics of the flaw on the initiation angles of wing cracks

the interactions between the filling materials and the surface of flaws were considered; the numerical analysis based on extended finite element method shows good agreements with theoretical analysis. The proposed method will provide a theoretical frame for the experimental analysis of mixed mode fractures under compression-shear loading experiments

and it also has a theory instruction function to the relevant experiments in the future.