Deformation behaviors and failure mechanisms of fully grouted bolts in jointed rock masses under coupled tension and shear

Fully grouted bolts are commonly used in mining and civil engineering for rock reinforcement, yet their bolting mechanisms, particularly in jointed rock mass, are not well-understood. Existing analytical methods often fail to accurately identify limit states under complex loads. In this study, dimensionless elastic and failure limit equations under tension and shear were derived, incorporating elastic–plastic bending theory with and without considering strain hardening effect. Strength envelopes for circular rebar were then illustrated. Taking the deflecting section of a fully-grouted bolt as a hyperstatic structure with ends rotation in the elastic stage and as a curved bar during the plastic stage, an improved tension-shear coupling beam (TSCB) model of the bolts was proposed. A computational program was developed to determine limit states through these strength envelopes. Results show that in the strain hardening stage, the bolt behaves like a slender rod rather than a truss. Mechanical analysis reveals that the bolt undergoes tension-shear failure at the bolt-joint intersection, with ongoing plastic deformation at the zero-shear force point, aligning with experimental observations. Comparison with experimental data confirms that the proposed method accurately predicts bolt contributions at both elastic and failure limits. This research significantly enhances bolting system design and stability assessment. Highlights. •Proposing an improved TSCB model of fully grouted bolts in jointed rock masses, which accurately describes bolts deformation behavior from elastic to strain hardening stages and identifies limit states under complex loads. •Deriving and illustrating dimensionless strength envelopes of circular rebar under complex loading conditions, which describe interaction relationships between coupled loads at limit states. •Determining the failure mode of fully grouted bolts under coupled tension and shear loads, i.e., tension-shear failure at the bolt-joint intersection, rather than tension-bending failure at other points along the deflecting section.