Cusp-Catastrophe-Based Evaluation of Critical Rockbolt–Grout Interface Debonding Displacement in Fully Grouted Rockbolts under Pull-Out Loading

Abstract

For a fully grouted rockbolt (FGR) subjected to pull-out loading, local instability may occur at the rockbolt–grout (R-G) interface when the surrounding medium is sufficiently stiff and the bolt–grout bond governs load transfer. This study derives a theoretical estimate for the shear displacement at which local R-G interface debonding is initiated. A biexponential nonlinear shear-slip relation is first formulated for the R-G interface from the load–displacement response and the load-transfer equation. The corresponding potential-energy expression is then constructed for the FGR system and locally reduced to the cusp catastrophe form near the critical state. The resulting instability condition provides an analytical estimate of the critical shear displacement at the onset of R-G interface debonding. Previously reported pull-out data are used only to check the consistency between the calculated critical displacement and the observed onset of interface loosening. The results indicate that the proposed model can describe the nonlinear softening tendency of the R-G interface and provide a theoretical reference for assessing debonding instability of FGR within the stated assumptions. Further model development is required before the criterion is applied to fractured rock, heterogeneous anchorage sections, grout–rock interface-controlled failure, or prestressed anchors containing an unbonded free length.