Abstract: Peridynamics (PD), as an emerging methodology, is demonstrating substantial potential as a means to analyze the mechanical responses of complex rock formations. However, the bond-based peridynamics method exhibits weak connections with continuum mechanics (CM). It cannot handle multiple fracture modes and post-peak behavior in rocks and significantly oversimplifies the contact-friction model. The calculation system of state-based peridynamics is more complex and less stable. Therefore, this paper proposed a quasi-state-based peridynamics method. This paper first achieves a simultaneous calculation of bond force density and stress tensor by employing a force density calculation method that distinguishes based on bond types, thereby deepening its association with continuum mechanics. Subsequently, a general criterion introduction approach (e.g., maximum tensile stress criterion and Mohr-Coulomb criterion) is provided, leading to the derivation of a single linear fictitious crack model suitable for the current theoretical framework. This enables a comprehensive simulation of multiple types of brittle failure in rock materials. Finally, using a particle mesh twin algorithm, binding fracture criterion and the discretization process of twin meshes, simultaneous calculations of material points and twin meshes in different medium states are accomplished. Through potential function and Coulomb's friction law, accurate assessments and characterizations of contact situations and degrees are achieved, incorporating friction force density calculations considering the friction coefficient. Case studies demonstrate a good agreement between simulation results and experimental outcomes. This signifies a significantly improved capability of the refined peridynamics in handling the formation-evolution processes of discontinuous media, thereby substantially broadening its original theoretical framework and applicability.