Peridynamics (PD) is an effective method for addressing fracture problems, yet it is hindered by high computational costs. The fast convolution-based method for peridynamics (FCBM-PD), which reconstructs the PD equations using the fast Fourier transform (FFT) algorithm, significantly improves computational efficiency. However, due to the differences in the implementation processes between FCBM-PD and traditional PD algorithms, suitable preprocessing methods for FCBM-PD are still lacking. In this paper, we propose a preprocessing method based on the Alpha shape algorithm, tailored to the specific characteristics of the FCBM-PD approach. We then apply this method to model random fractures and use the FCBM-PD technique to predict fracture propagation in a two-dimensional random fracture model. The accuracy of the model is validated through comparisons with traditional PD models. The preprocessing method presented in this study may facilitate the broader application of FCBM-PD in geotechnical engineering.