Quasi-brittle fracture in geo-materials plays a crucial role in geotechnical engineering, and numerical methods represent a valuable approach for modeling this complex problem. This study introduces a mixed bilinear failure model considering bond effects in a modified Discontinuous Deformation Analysis (DDA) framework. Several benchmark crack-propagation problems for different materials and geometries, including three-point beam, Lshaped structure, semi-disc test and cemented granular packing, are presented to validate the novel DDA method proposed in this study. The simulation results show the accuracy of the model in predicting the mixed-mode failure of quasi-brittle materials with complex structures and assess its great potential for investigating the mechanical properties of geo-materials.

The mechanical properties of coarse granular materials play a crucial role in the safety of rockfill dams. From a mesoscopic viewpoint, the macroscopic mechanical properties of these materials are a result of the interactions between particles and the progression of particle breakage. Traditional continuum-based numerical methods struggle to accurately analyze the mechanical properties of coarse granular materials. Discontinuous deformation analysis (DDA) is a more suitable algorithm for studying these properties due to its significant benefits in block displacement mode and open-close iteration for contact handling. In this paper, a continuous-discontinuous deformation analysis method (CDDA) based on the conventional DDA is developed for the numerical investigation of coarse granular materials' mechanical properties. This method incorporates critical kinetic damping, multi-stage loading, stricter displacement convergence criteria and particle breakage simulation. It can provide a comprehensive representation of deformation, particle breakage, force chain, shear zone, and stress-strain curve evolutions. The CDDA results are found to be consistent with indoor test results and can more effectively disclose the deformation and failure mechanism of coarse granular materials. Furthermore, CDDA is employed to examine the impacts of particle size and end friction, leading to valuable insights regarding these effects.

This paper presents an improved longitudinal beam-spring model on the Vlasov foundation for estimating the longitudinal deformation of the shield tunnel when subjected to the ground surface surcharge. This model incorporates an improved subgrade modulus and treats each segmental ring as a Timoshenko short beam, with each circumferential joint modeled by two mechanical springs. It can accurately reflect the discontinuous deformation, and capture the dislocation and opening deformation of shield tunnels. Two-stage analysis methodology is adopted to consider soil and tunnel interaction. The feasibility of this model is verified by comparing it with two well-documented field monitoring cases. The computed results are also compared with those based on other analytical models. The results show that the Timoshenko continuous beam overestimates the dislocation deformation, while underestimates the opening deformation. In addition, the settlement curve exhibits neither smooth nor differentiable features. Finally, this paper also conducted some parameter analysis to examine the impact on tunnel deformation, encompassing dimensions of ground surface surcharge, the dual-area loading, and the joint reinforcement. This approach provides valuable insights into how the deformation characteristics of shield tunnels are influenced by ground surface surcharge.