Numerical investigation and experimental study on fracture processes of central flawed sandstone Brazilian discs

•An improved SPH method was introduced, which can be applied to the modeling of rock fracture modeling.•The penalty force algorithm of boundary particles was developed to realize the application of displacement boundaries in SPH.•Experiments on red sandstone Brazilian disc combined with DIC technology were carried out, and the crack propagation processes were obtained.•The crack propagation mechanisms were discussed combined with the improved SPH method and experimental results.