In the domain of shield tunneling, the auxiliary pre-grouting technique plays a crucial role in mitigating the instability of tunneling face in sandy strata, arising primarily from factors such as soil properties and excavation-induced disturbances. The intricacies involved in monitoring grouting bulbs and the immediate interaction between grout and strata emphasize the necessity for more comprehensive studies. This research aims to elucidate the underlying mechanisms governing the grouting process on the tunneling face using the Discrete Element Method (DEM). The primary focus is on understanding the dispersion dynamics of frictionless grouting slurry particles and their subsequent impact on the stress-displacement response of surrounding soil. Subsequently, the passive stability of grouted tunnel faces is evaluated by employing the classical logarithmic spiral potential failure model, revealing a decreasing trend of angles theta(A) (from 85 degrees to 45 degrees ) and 0 theta(B) (from 50 degrees to 10 degrees), and predicted critical supporting pressure with increasing injected grouting material. Furthermore, the research identifies and proposes an optimization to address the inherent geometric limitations of the logarithmic spiral model by incorporating an extended envelope range.