Analytical modeling of mechanical response and ultimate failure of a grouted rockbolt with a single corrosion pit
A single corrosion pit in a grouted rockbolt should be mechanically interpreted as a localized weakened segment, because it introduces a discontinuity in axial stiffness, disturbs the dominant load-transfer zone near the loaded end, and complicates the ultimate failure behavior of the anchorage system. To clarify this mechanism, a three-segment analytical model is developed, in which the pit-corroded portion is equivalently represented as a locally weakened segment between two intact segments. Under the assumptions of compatible axial deformation between the rockbolt and grout and linear shear transfer at the grout-rock interface, analytical solutions for axial displacement, total axial force, and interfacial shear stress are derived using the state vector and transfer matrix method. The model is validated by numerical simulation and then used to investigate the effects of pit geometry, material modulus degradation, and external load-transfer parameters. The results show that the principal effect of a single corrosion pit is the disturbance of the front-segment load-transfer zone caused by local stiffness reduction, leading to the redistribution of displacement, axial-force attenuation, and interfacial shear-stress evolution. Among the corrosion-related parameters, pit length and material modulus degradation exert the strongest influence on response deterioration, whereas pit depth mainly governs the local fracture susceptibility of the weakened segment. Two ultimate bearing-capacity criteria are further established for interface slip-debonding and weakened-segment fracture, and the final bearing capacity is determined by the competition between these two failure modes. This study provides a mechanistic basis for the assessment of locally pit-corroded grouted rockbolts.